コンクリートおよび岩石材料 コンクリート材料(/MAT/LAW24) 鉄筋コンクリート材料をモデル化するには、降伏におけるcapの有無によらず、LAW24でDrücker-Prager基準を使用します。この材料則では、コンクリート材料の破壊メカニズムとして引張亀裂と圧縮破砕の2つを想定しています。 コンクリートの引張挙動 LAW24では、引張時に、オプションHt、Dsup、および ε max を使用して、引張亀裂と引張破壊を表すことができます。 図 1. LAW24引張荷重 初期の非常に小さな弾性相においては、材料は弾性係数Ecを有します。 引張強度ftに達すると、コンクリートはHtの勾配で軟化し始めます。最大損傷係数Dsupは、亀裂中および亀裂後の残留剛性のモデル化を可能にするため重要です。 図 2. 最大損傷係数の影響 残留剛性は次のように計算されます:(1) E=( 1− D sup )⋅ E c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGfbGaey ypa0ZaaeWaaeaacaaIXaGaeyOeI0IaamiramaaBaaaleaaciGGZbGa aiyDaiaacchaaeqaaaGccaGLOaGaayzkaaGaeyyXICTaamyramaaBa aaleaacaWGJbaabeaaaaa@436C@ 亀裂閉口が生じると、コンクリートは再度弾性となり、(各方向の)損傷係数は維持されます。 引張におけるコンクリートの支持力は、圧縮における支持力よりはるかに小さくなります。引張では、通常これは弾性と見なされます。 損傷の端における現在の剛性を最小化し、それによって引張における残留応力を回避するため、1に近いDsup値(デフォルトでは0.99999)を選択することをお勧めします。 残留応力は、引張による要素の変形が非常に大きい場合、かなり大きくなる場合があります。これは、損傷の原因になった力が残存している場合に発生します。 繊維によって補強されたコンクリートの挙動をシミュレートし、フィッティングするには、Dsup(およびHt)を調整することができます。全破壊ひずみ ε max に達すると、コンクリート材料は破壊します。 圧縮におけるコンクリートの降伏曲面 コンクリートの場合、降伏曲面は、破壊曲面 r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbWaaS baaSqaaiaadAgaaeqaaaaa@386C@ と降伏曲面の間である塑性硬化ゾーンの始まりです。 降伏曲面は、引張ゾーンでの破壊曲面と同じと見なされます。圧縮では、降伏曲面が係数 k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaaaa@3E53@ を使用して破壊曲面にスケールダウンされます。コンクリートのLAW24での降伏は、以下のとおりです:(2) f = r ︸ J 2 p a r t − k ( σ m , k 0 ) ⋅ r f ︸ I 1 p a r t = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbGaey ypa0ZaaGbaaeaacaWGYbaalqaabeqaaiaadQeadaWgaaadbaGaaGOm aaqabaaaleaacaWGWbGaamyyaiaadkhacaWG0baaaOGaayjo+dGaey OeI0YaaGbaaeaaciGGRbWaaeWaaeaacqaHdpWCdaWgaaWcbaGaamyB aaqabaGccaGGSaGaam4AamaaBaaaleaacaaIWaaabeaaaOGaayjkai aawMcaaiabgwSixlaadkhadaWgaaWcbaGaamOzaaqabaaabaGaamys amaaBaaameaacaaIXaaabeaaluaabeqabeaaaeaaaaGaamiCaiaadg gacaWGYbGaamiDaaGccaGL44pacqGH9aqpcaaIWaaaaa@5761@ Icap =0または1(降伏におけるcapなし)の場合、降伏曲線は以下のようになります: 図 3. 降伏におけるcapなしでのDrücker-Prager基準 Icap =2(降伏におけるcapあり)の場合、降伏は以下のようになります: 図 4. 降伏におけるcapありでのDrücker-Prager基準 r < k ( σ m , k 0 ) ⋅ r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey ipaWJaci4AamaabmaabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGa aiilaiaadUgadaWgaaWcbaGaaGimaaqabaaakiaawIcacaGLPaaacq GHflY1caWGYbWaaSbaaSqaaiaadAgaaeqaaaaa@44A6@ (図 4の緑色の領域) 材料は弾性相に属し、降伏には達していません。 r ≥ r f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey yzImRaamOCamaaBaaaleaacaWGMbaabeaaaaa@3B2A@ (図 4の赤色の領域) 材料は破壊されています。 k ( σ m , k 0 ) ⋅ r f < r < r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabgwSixlaadkhada WgaaWcbaGaamOzaaqabaGccqGH8aapcaWGYbGaeyipaWJaamOCamaa BaaaleaacaWGMbaabeaaaaa@47C2@ (図 4の黄色の領域) 材料は、降伏曲面より上で破壊曲面より下の、塑性硬化相に属しています。 入力パラメータ ρ t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaamiDaaqabaaaaa@3943@ は単軸引張試験における破壊静水圧、 ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaamiDaaqabaaaaa@3943@ は単軸圧縮試験における破壊時の静水圧です。 スケールファクター k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaaaa@3E53@ は、平均応力 σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaaaaa@393F@ の関数であり、以下のように表すことができます: σ m ≥ ρ t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaGccqGHLjYScqaHbpGCdaWgaaWcbaGaamiD aaqabaaaaa@3DF4@ (引張)の場合、スケールファクターは k ( σ m , k 0 ) = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaigdaaa a@4014@ です。この場合、降伏曲面は破壊曲面と等しくなります: r= r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey ypa0JaamOCamaaBaaaleaacaWGMbaabeaaaaa@3A69@ 図 5. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ (引張ゾーンにおける) 引張-圧縮領域において、 ρ t > σ m ≥ ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaamiDaaqabaGccqGH+aGpcqaHdpWCdaWgaaWcbaGaamyB aaqabaGccqGHLjYScqaHbpGCdaWgaaWcbaGaam4yaaqabaaaaa@41DA@ の場合、 k ( σ m , k 0 ) = 1 + ( 1 − k 0 ) ⋅ [ ρ t ( 2 ρ c − ρ t ) − 2 ρ c σ m + σ m 2 ] ( ρ c − ρ t ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaigdacq GHRaWkdaWcaaqaamaabmaabaGaaGymaiabgkHiTiaadUgadaWgaaWc baGaaGimaaqabaaakiaawIcacaGLPaaacqGHflY1daWadaqaaiabeg 8aYnaaBaaaleaacaWG0baabeaakmaabmaabaGaaGOmaiabeg8aYnaa BaaaleaacaWGJbaabeaakiabgkHiTiabeg8aYnaaBaaaleaacaWG0b aabeaaaOGaayjkaiaawMcaaiabgkHiTiaaikdacqaHbpGCdaWgaaWc baGaam4yaaqabaGccqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGHRa WkcqaHdpWCdaWgaaWcbaGaamyBaaqabaGcdaahaaWcbeqaaiaaikda aaaakiaawUfacaGLDbaaaeaadaqadaqaaiabeg8aYnaaBaaaleaaca WGJbaabeaakiabgkHiTiabeg8aYnaaBaaaleaacaWG0baabeaaaOGa ayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaaaaaa@6B9F@ ここで、 k y ≤ k 0 ≤ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaOGaeyizImQaam4AamaaBaaaleaacaaIWaaa beaakiabgsMiJkaaigdaaaa@3E87@ 図 6. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 圧縮-引張混合ゾーンでの関数 曲線の残りは、Icapオプションに依存し、異なるスケールファクター k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaaaa@3E53@ が使用されます。 Icap =0または1、かつ σ m < ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaGccqGH8aapcqaHbpGCdaWgaaWcbaGaam4y aaqabaaaaa@3D21@ (圧縮)の場合、 k ( σ m , k 0 ) = k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaadUgada WgaaWcbaGaamyEaaqabaaaaa@4173@ 図 7. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 圧縮ゾーンでの関数 Icap =2(降伏におけるcapあり)、かつ ρ c < σ m < f k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaam4yaaqabaGccqGH8aapcqaHdpWCdaWgaaWcbaGaamyB aaqabaGccqGH8aapcaWGMbWaaSbaaSqaaiaadUgaaeqaaaaa@4036@ (圧縮)の場合、 k ( σ m , k 0 ) = k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaadUgada WgaaWcbaGaamyEaaqabaaaaa@4173@ 図 8. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ capなしのDrücker-Prager基準の関数 f k < σ m < f 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadUgaaeqaaOGaeyipaWJaeq4Wdm3aaSbaaSqaaiaad2ga aeqaaOGaeyipaWJaamOzamaaBaaaleaacaaIWaaabeaaaaa@3F33@ (capゾーン内)において、 k ( σ m , k 0 ) = k 0 [ 1 − ( σ m − f k f 0 − f k ) 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaadUgada WgaaWcbaGaaGimaaqabaGcdaWadaqaaiaaigdacqGHsisldaqadaqa amaalaaabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaeyOeI0Iaam OzamaaBaaaleaacaWGRbaabeaaaOqaaiaadAgadaWgaaWcbaGaaGim aaqabaGccqGHsislcaWGMbWaaSbaaSqaaiaadUgaaeqaaaaaaOGaay jkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2faaaaa @5221@ ここで、 0 ≤ k 0 ≤ k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaGaey izImQaam4AamaaBaaaleaacaaIWaaabeaakiabgsMiJkaadUgadaWg aaWcbaGaamyEaaqabaaaaa@3E7C@ 図 9. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ capありのDrücker-Prager基準の関数 材料定数 k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaaaa@3878@ は、 0 ≤ k y ≤ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaGaey izImQaam4AamaaBaaaleaacaWG5baabeaakiabgsMiJkaaigdaaaa@3D61@ である必要があります。大きな値の k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaaaa@3878@ では、降伏曲面がより高くなります。 例えばIcap =2(capのある降伏)の場合、 k y = 0.8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaOGaeyypa0JaaGimaiaac6cacaaI4aaaaa@3BB6@ と k y = 0.6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaOGaeyypa0JaaGimaiaac6cacaaI2aaaaa@3BB4@ の降伏曲面の違い(図 10)。LAW24における k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaaaa@3878@ のデフォルト値は0.5です。 図 10. 異なる k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 関数値の影響 図 11. 異なる k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 関数値によるDrücker-Prager基準 圧縮におけるコンクリートの塑性流れ則 非関連塑性流れ則はLAW24で使用されます。塑性流れ則は以下のとおりです:(3) g=α I 1 + J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGNbGaey ypa0JaeqySdeMaamysamaaBaaaleaacaaIXaaabeaakiabgUcaRmaa kaaabaGaamOsamaaBaaaleaacaaIYaaabeaaaeqaaaaa@3E57@ ここで、 α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ 塑性域のダイラタンシー。 α = ∂ g ∂ I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpdaWcaaqaaiabgkGi2kaadEgaaeaacqGHciITcaWGjbWaaSba aSqaaiaaigdaaeqaaaaaaaa@3E80@ 体積塑性流れを制御します。 I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaaigdaaeqaaaaa@3813@ 第1応力不変量(静水圧)。 実験に基づいて、 α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ は、 k 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaaaa@3834@ の線形関数です:(4) α = ( 1 − k 0 ) α y + ( k 0 − K y ) α f 1 − K y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpdaWcaaqaamaabmaabaGaaGymaiabgkHiTiaadUgadaWgaaWc baGaaGimaaqabaaakiaawIcacaGLPaaacqaHXoqydaWgaaWcbaGaam yEaaqabaGccqGHRaWkdaqadaqaaiaadUgadaWgaaWcbaGaaGimaaqa baGccqGHsislcaWGlbWaaSbaaSqaaiaadMhaaeqaaaGccaGLOaGaay zkaaGaeqySde2aaSbaaSqaaiaadAgaaeqaaaGcbaGaaGymaiabgkHi TiaadUeadaWgaaWcbaGaamyEaaqabaaaaaaa@4E95@ 次の場合; k 0 = K y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaOGaeyypa0Jaam4samaaBaaaleaacaWG5baa beaaaaa@3B3E@ α = α y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpcqaHXoqydaWgaaWcbaGaamyEaaqabaaaaa@3BCC@ となり、材料が降伏していることを意味します。 次の場合; k 0 < K y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaOGaeyipaWJaam4samaaBaaaleaacaWG5baa beaaaaa@3B3C@ α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ は、cap領域で負となります。 次の場合; k 0 = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaOGaeyypa0JaaGymaaaa@39FF@ α = α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpcqaHXoqydaWgaaWcbaGaamOzaaqabaaaaa@3BB9@ となり、材料が破壊されていることを意味します。 α y , α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyEaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3D3A@ の値は、降伏点を超え、破壊前の材料を表すために使用されます。LAW24では、 α y , α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyEaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3D3A@ に-0.2および-0.1を使用することをお勧めします。 α y , α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyEaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3D3A@ に非常に小さな値が使用されると、体積塑性はなくなります(cap領域なし)。 圧縮におけるコンクリートの圧壊 破壊サーフェスは次のように与えられます: (5) f=r− r f ( σ m ,θ)=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2 da9iaadkhacqGHsislcaWGYbWaaSbaaSqaaiaadAgaaeqaaOGaaiik aiabeo8aZnaaBaaaleaacaWGTbaabeaakiaacYcacqaH4oqCcaGGPa Gaeyypa0JaaGimaaaa@444D@ ここで、 r = 2 J 2 / f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaadQeadaWgaaWcbaGaaGOmaaqabaaabeaa kiaac+cacaWGMbWaaSbaaSqaaiaadogaaeqaaaaa@3D32@ , σ m = I 1 / 3 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaamysamaaBaaaleaacaaIXaaa beaakiaac+cacaaIZaGaamOzamaaBaaaleaacaWGJbaabeaaaaa@3F15@ と θ はLoad角で、次のようになります:(6) cos3θ= J 3 2 ( 3 J 2 ) 3/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaaG4maiabeI7aXjabg2da9maalaaabaGaamOsamaaBaaa leaacaaIZaaabeaaaOqaaiaaikdaaaWaaeWaaeaadaWcaaqaaiaaio daaeaacaWGkbWaaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaawMca amaaCaaaleqabaGaaG4maiaac+cacaaIYaaaaaaa@4540@ このサーフェスを構築するためにOttosenサーフェスが作成されます: (7) r f ( σ m ,θ)= 1 a ( −b+ b 2 −a( σ m −c ) ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaBa aaleaacaWGMbaabeaakiaacIcacqaHdpWCdaWgaaWcbaGaamyBaaqa baGccaGGSaGaeqiUdeNaaiykaiabg2da9maalaaabaGaaGymaaqaai aadggaaaWaaeWaaeaacqGHsislcaWGIbGaey4kaSYaaOaaaeaacaWG IbWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaamyyamaabmaabaGaeq 4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaeyOeI0Iaam4yaaGaayjkaiaa wMcaaaWcbeaaaOGaayjkaiaawMcaaaaa@4FC9@ ここで、 a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaaaa@36DC@ 、 b c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGJbaabeaaaaa@37F1@ 、 b t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGJbaabeaaaaa@37F1@ および c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yaaaa@36DE@ がサーフェスを形成する4つの値で、 (8) b ( b c , b t , θ ) = 1 2 [ b c ( 1 − cos 3 θ ) + b t ( 1 + cos 3 θ ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaabm aabaGaamOyamaaBaaaleaacaWGJbaabeaakiaacYcacaWGIbWaaSba aSqaaiaadshaaeqaaOGaaiilaiabeI7aXbGaayjkaiaawMcaaiabg2 da9maalaaabaGaaGymaaqaaiaaikdaaaWaamWaaeaacaWGIbWaaSba aSqaaiaadogaaeqaaOWaaeWaaeaacaaIXaGaeyOeI0Iaci4yaiaac+ gacaGGZbGaaG4maiabeI7aXbGaayjkaiaawMcaaiabgUcaRiaadkga daWgaaWcbaGaamiDaaqabaGcdaqadaqaaiaaigdacqGHRaWkciGGJb Gaai4BaiaacohacaaIZaGaeqiUdehacaGLOaGaayzkaaaacaGLBbGa ayzxaaaaaa@59F6@ コンクリートの場合、圧縮破壊曲線 r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbWaaS baaSqaaiaadAgaaeqaaaaa@386C@ は、以下の強度で定義できます。 f t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaaaa@386E@ 単軸引張(軸性は1/3) f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaaaa@386E@ 単軸圧縮(軸性は-1/3) f b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaaaa@386E@ 2軸圧縮(軸性は-2/3) f 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAgadaWgaaWcbaGaaGOmaaqabaaaaa@3B28@ 拘束圧縮強度(3軸試験) s 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadohadaWgaaWcbaGaaGimaaqabaaaaa@3B33@ 拘束圧 3D破壊エンベロープをすべて特定する最善の方法は、 f c , f t , f b , f 2 , s 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAgadaWgaaWcbaGaam4yaaqabaGccaGGSaGaamOzamaaBaaa leaacaWG0baabeaakiaacYcacaWGMbWaaSbaaSqaaiaadkgaaeqaaO GaaiilaiaadAgadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaam4Camaa BaaaleaacaaIWaaabeaaaaa@45FB@ のすべての値の実験データを取得する方法です。これを図 12に図式的に示します。 図 12. 3D破壊エンベロープをすべて特定する破壊パラメータ 表 1. 4つの実験からの入力 荷重タイプ サーフェスポイント デフォルト入力 基準 r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@36ED@ 圧力 σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaaaa@38D7@ Lode角 θ 圧縮 ( f c , 0 , 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaai aadAgadaWgaaWcbaGaam4yaaqabaGccaGGSaGaaGimaiaacYcacaaI WaaacaGLOaGaayzkaaaaaa@3DCE@ 必須 r= 2/3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaaaa@3A3A@ σ m =−1/3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaeyOeI0IaaGymaiaac+cacaaI Zaaaaa@3CFF@ cosθ=−1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaeyOeI0IaaGymaaaa@3D2D@ 直接引っ張り ( f t , 0 , 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaai aadAgadaWgaaWcbaGaam4yaaqabaGccaGGSaGaaGimaiaacYcacaaI WaaacaGLOaGaayzkaaaaaa@3DCE@ f t =0 .1 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaOGaaeypaiaabcdacaqGUaGaaeymaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E59@ r= 2/3 ( f t f c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaOWaaeWaaeaadaWc aaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMbWaaSbaaS qaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaaaa@4000@ σ m =1/3( f t f c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaaGymaiaac+cacaaIZaWaaeWa aeaadaWcaaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMb WaaSbaaSqaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaaaa@41CE@ cosθ=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaaGymaaaa@3C40@ 2軸圧縮 ( f 2 , s 0 , s 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaai aadAgadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaam4CamaaBaaaleaa caaIWaaabeaakiaacYcacaWGZbWaaSbaaSqaaiaaicdaaeqaaaGcca GLOaGaayzkaaaaaa@3FFE@ Icap = 1であれば、 f 2 =4 .0 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaaikdaaeqaaOGaaeypaiaabsdacaqGUaGaaeimaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E1F@ Icap = 2であれば、 f 2 =7 .0 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaaikdaaeqaaOGaaeypaiaabsdacaqGUaGaaeimaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E1F@ s 0 =1.25 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGZbWaaS baaSqaaiaaicdaaeqaaOGaaeypaiaabgdacaqGUaGaaeOmaiaabwda caWGMbWaaSbaaSqaaiaadogaaeqaaaaa@3EE1@ r= 2/3 ( f t f c ) σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaOWaaeWaaeaadaWc aaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMbWaaSbaaS qaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaiabeo8aZnaaBaaaleaa caWGTbaabeaaaaa@42E1@ σ m = 2 / 3 ( f t f c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaaGymaiaac+cacaaIZaWaaeWa aeaadaWcaaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMb WaaSbaaSqaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaaaa@41CE@ cos θ = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaaGymaaaa@3C40@ 拘束圧力の下での圧縮強度 ( f b , f b , 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeGabaaUfmaabm aabaGaamOzamaaBaaaleaacaWGIbaabeaakiaacYcacaWGMbWaaSba aSqaaiaadkgaaeqaaOGaaiilaiaaicdaaiaawIcacaGLPaaaaaa@3FDB@ f b =1.2 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadkgaaeqaaOGaaeypaiaabgdacaqGUaGaaeOmaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E49@ r= 2/3 f 2 − s 0 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaOWaaSaaaeaacaWG MbWaaSbaaSqaaiaaikdaaeqaaOGaeyOeI0Iaam4CamaaBaaaleaaca aIWaaabeaaaOqaaiaadAgadaWgaaWcbaGaam4yaaqabaaaaaaa@4105@ σ m = f 2 +2 s 0 3 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0ZaaSaaaeaacaWGMbWaaSbaaSqa aiaaikdaaeqaaOGaey4kaSIaaGOmaiaadohadaWgaaWcbaGaaGimaa qabaaakeaacaaIZaGaamOzamaaBaaaleaacaWGJbaabeaaaaaaaa@4216@ cos θ = − 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaeyOeI0IaaGymaaaa@3D2D@ 図 13 と図 14は、破壊サーフェスを決定するポイントを示しています。 図 13. 平坦な応力面を有する破壊サーフェスのトレース 図 14. 静水圧軸に垂直な複数の断面を有する破壊トレース これらのプロットから、破壊エンベロープが凸型サーフェスではないことがわかります。 図 15 はこの挙動を示しています。 図 15. 2軸圧縮強度値の影響: 作用点以外の、特性に影響するすべての破壊点を固定した状態 図 16. 圧縮強度値の影響: 作用点以外の、特性に影響するすべての破壊点を固定した状態 図 17. 引張強度値の影響: 作用点以外の、特性に影響するすべての破壊点を固定した状態 この特定のケースにおいては、圧縮強度は変化していますが、 f t f c , f b f c , f 2 f c , s 0 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGaaeaaca WGMbWaaSbaaSqaaiaadshaaeqaaaGcbaGaamOzamaaBaaaleaacaWG JbaabeaaaaGccaGGSaGaaeiiamaaliaabaGaamOzamaaBaaaleaaca WGIbaabeaaaOqaaiaadAgadaWgaaWcbaGaam4yaaqabaaaaOGaaiil aiaabccadaWccaqaaiaadAgadaWgaaWcbaGaaGOmaaqabaaakeaaca WGMbWaaSbaaSqaaiaadogaaeqaaaaakiaabYcacaqGGaWaaSGaaeaa caWGZbWaaSbaaSqaaiaaicdaaeqaaaGcbaGaamOzamaaBaaaleaaca WGJbaabeaaaaaaaa@4A37@ といったその他すべての比率は固定されています。これにより、図 18のようなエンベロープスケーリングが生じます。 図 18. 圧縮強度値の影響. 他のすべての比率は固定。 ここでは、LAW24と同じ強度を使用していますが、拘束圧縮強度 f 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaaikdaaeqaaaaa@393B@ には異なる値を使用しています。 図 19. 3軸破壊点 ( σ 1 , σ 2 , σ 3 ) = ( f 2 , s 0 , s 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaamaabmaabaGaeq4Wdm3aaSbaaSqaaiaaigdaaeqaaOGaaiilaiab eo8aZnaaBaaaleaacaaIYaaabeaakiaacYcacqaHdpWCdaWgaaWcba GaaG4maaqabaaakiaawIcacaGLPaaacqGH9aqpdaqadaqaaiaadAga daWgaaWcbaGaaGOmaaqabaGccaGGSaGaam4CamaaBaaaleaacaaIWa aabeaakiaacYcacaWGZbWaaSbaaSqaaiaaicdaaeqaaaGccaGLOaGa ayzkaaaaaa@4DF9@ の影響を受ける平坦な応力面上の破壊エンベロープ f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadogaaeqaaaaa@385D@ 、およびコンクリート破壊の定義に使用する r − σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey OeI0Iaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaaaa@3B23@ 空間での比率 f t f c , and f b f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWccaqaai aadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMbWaaSbaaSqaaiaa dogaaeqaaaaakiaacYcacaqGGaGaaeyyaiaab6gacaqGKbGaaeiiam aaliaabaGaamOzamaaBaaaleaacaWGIbaabeaaaOqaaiaadAgadaWg aaWcbaGaam4yaaqabaaaaaaa@435E@ は次のようになります: 図 20. 破壊曲線を決定するための各種試験(単軸引張、単軸圧縮、および2軸圧縮) ここで、破壊曲線は、 r = 2 J 2 = 2 3 σ V M MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey ypa0ZaaOaaaeaacaaIYaGaamOsamaaBaaaleaacaaIYaaabeaaaeqa aOGaeyypa0ZaaOaaaeaadaWcaaqaaiaaikdaaeaacaaIZaaaaaWcbe aakiabeo8aZnaaBaaaleaacaWGwbGaamytaaqabaaaaa@4138@ を使用して定義され、 σ m = I 1 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaGccqGH9aqpdaWcaaqaaiaadMeadaWgaaWc baGaaGymaaqabaaakeaacaaIZaaaaaaa@3CDB@ は平均応力(圧力)、 I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaaigdaaeqaaaaa@3813@ および J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaaigdaaeqaaaaa@3813@ は第1および第2応力不変量です。 破壊曲線 r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbWaaS baaSqaaiaadAgaaeqaaaaa@386C@ に達すると、材料は破壊します。 コンクリートの補強Radiossでは、2つの方法でコンクリートの補強をシミュレートできます。 1つは、ビームまたはトラス要素を複数の運動条件でコンクリートに結合する方法です。 もう1つは、LAW24のパラメータを直交異方性ソリッドプロパティ/PROP/TYPE6とともに使用し、補強方向を定義する方法です。LAW24のパラメータ α 1 , α 2 , α 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaaGymaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caaIYaaabeaakiaacYcacaqGGaGaeqySde2aaSbaaSqaaiaaiodaae qaaaaa@40AD@ を使用して、方向1、2、3について、全体のコンクリート断面積に対する補強断面積の比率を定義します。(9) α i = A r e a s t e e l A r e a c o n c r e t e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyAaaqabaGccqGH9aqpdaWcaaqaaiaadgeacaWGYbGa amyzaiaadggadaWgaaWcbaGaam4CaiaadshacaWGLbGaamyzaiaadY gaaeqaaaGcbaGaamyqaiaadkhacaWGLbGaamyyamaaBaaaleaacaWG JbGaam4Baiaad6gacaWGJbGaamOCaiaadwgacaWG0bGaamyzaaqaba aaaaaa@4DE4@ ここで、 σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyEaaqabaaaaa@394B@ は、補強の降伏応力です。補強としてスチールが使用される場合は、 σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyEaaqabaaaaa@394B@ がスチールの降伏応力で、 E t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGfbWaaS baaSqaaiaadshaaeqaaaaa@384D@ が塑性相におけるスチールの弾性率です。 図 21. 補強(スチール)の応力-ひずみ曲線 コンクリート材料(/MAT/LAW81) LAW81は岩石またはコンクリート材料のモデル化に使用できます。 Drücker-Prager降伏基準 LAW81ではDrücker-Prager降伏基準を使用します。ここでは、降伏曲面と破壊曲面が同じです。降伏基準は以下のとおりです:(10) F = q ︸ J 2 part − r c ( p ) ⋅ ( p tan ϕ + c ) ︸ I 1 part = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbGaey ypa0ZaaGbaaeaacaWGXbaaleaacaWGkbWaaSbaaWqaaiaaikdaaeqa aSGaaeiiaiaabchacaqGHbGaaeOCaiaabshaaOGaayjo+dGaeyOeI0 YaaGbaaeaaciGGYbWaaSbaaSqaaiaacogaaeqaaOWaaeWaaeaacaWG WbaacaGLOaGaayzkaaGaeyyXIC9aaeWaaeaacaWGWbGaciiDaiaacg gacaGGUbGaeqy1dyMaey4kaSIaam4yaaGaayjkaiaawMcaaaWcbaGa amysamaaBaaameaacaaIXaaabeaaliaabccacaqGWbGaaeyyaiaabk hacaqG0baakiaawIJ=aiabg2da9iaaicdaaaa@5BE0@ ここで、 q MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ 以下の条件におけるvon Mises応力: q = σ V M = 3 J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0Jaeq4Wdm3aaSbaaSqaaiaadAfacaWGnbaabeaakiabg2da9maa kaaabaGaaG4maiaadQeadaWgaaWcbaGaaGOmaaqabaaabeaaaaa@3F8A@ p MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ 圧力は以下のように定義されます: p = 1 3 I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey ypa0ZaaSaaaeaacaaIXaaabaGaaG4maaaacaWGjbWaaSbaaSqaaiaa igdaaeqaaaaa@3B96@ 図 22. 降伏曲面(LAW81) 降伏曲面は2つの部分で表されます: 線形部分( p ≤ p a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey izImQaamiCamaaBaaaleaacaWGHbaabeaaaaa@3B0F@ )、ここではスケール関数が r c ( p ) = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGYbWaaS baaSqaaiaacogaaeqaaOWaaeWaaeaacaWGWbaacaGLOaGaayzkaaGa eyypa0JaaGymaaaa@3CB2@ で、von Mises応力が圧力に線形比例します:(11) q = p tan ϕ + c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0JaamiCaiGacshacaGGHbGaaiOBaiabew9aMjabgUcaRiaadoga aaa@3FB2@ ここで、 c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ 粘度。せん断強度による降伏エンベロープを制限します。 c = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGJbGaey ypa0JaaGimaaaa@3906@ の場合、材料に引張強度はありません。 ϕ 内部摩擦の角度。降伏エンベロープの勾配を定義します。 c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ および ϕ は、Mohr-Coulomb降伏曲面の定義にも使用されます。Drücker-Prage降伏曲面は、Mohr-Coulomb降伏曲面を滑らかにしたものです。 降伏曲面の2つ目の部分( p a < p < p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadggaaeqaaOGaeyipaWJaamiCaiabgYda8iaadchadaWg aaWcbaGaamOyaaqabaaaaa@3D74@ )は、cap制限をシミュレートします。岩石またはコンクリート材料での圧力の増加により、材料の降伏が増加しますが、圧力が十分に大きくなると、岩石またはコンクリート材料は圧壊されます。cap制限のあるDrücker-Pragerモデルを使用して、この挙動をモデル化できます。cap制限はの部分で定義され、以下のスケール関数を使用します:(12) r c ( p ) = 1 − ( p − p a p b − p a ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGYbWaaS baaSqaaiaacogaaeqaaOWaaeWaaeaacaWGWbaacaGLOaGaayzkaaGa eyypa0ZaaOaaaeaacaaIXaGaeyOeI0YaaeWaaeaadaWcaaqaaiaadc hacqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGcbaGaamiCamaa BaaaleaacaWGIbaabeaakiabgkHiTiaadchadaWgaaWcbaGaamyyaa qabaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaqabaaa aa@4934@ von Mises応力は以下のようになります:(13) q = 1 − ( p − p a p b − p a ) 2 ⋅ ( p tan ϕ + c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0ZaaOaaaeaacaaIXaGaeyOeI0YaaeWaaeaadaWcaaqaaiaadcha cqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGcbaGaamiCamaaBa aaleaacaWGIbaabeaakiabgkHiTiaadchadaWgaaWcbaGaamyyaaqa baaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaqabaGccq GHflY1daqadaqaaiaadchaciGG0bGaaiyyaiaac6gacqaHvpGzcqGH RaWkcaWGJbaacaGLOaGaayzkaaaaaa@50CC@ ここで、 p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadkgaaeqaaaaa@3866@ 曲線はfct_IDPb入力を使用して定義されます。 p a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadkgaaeqaaaaa@3866@ 入力 α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ 率の値を使用してRadiossによって計算されます。 p a = α ⋅ p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadggaaeqaaOGaeyypa0JaeqySdeMaeyyXICTaamiCamaa BaaaleaacaWGIbaabeaaaaa@3F66@ ここで、 0 < α < 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaGaey ipaWJaeqySdeMaeyipaWJaaGymaaaa@3B7A@ 。 ここで、 p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ は、降伏曲線の最大ポイントです。ここで、 ∂ F ∂ p ( p 0 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kaadAeaaeaacqGHciITcaWGWbaaamaabmaabaGaamiCamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaicdaaa a@4028@ p = p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey ypa0JaamiCamaaBaaaleaacaWGIbaabeaaaaa@3A61@ の場合、 r c ( p b ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGYbWaaS baaSqaaiaacogaaeqaaOWaaeWaaeaacaWGWbWaaSbaaSqaaiaadkga aeqaaaGccaGLOaGaayzkaaGaeyypa0JaaGimaaaa@3DCE@ となり、降伏関数は、 q = 0 ⋅ ( p tan ϕ + c ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0JaaGimaiabgwSixpaabmaabaGaamiCaiGacshacaGGHbGaaiOB aiabew9aMjabgUcaRiaadogaaiaawIcacaGLPaaacqGH9aqpcaaIWa aaaa@45FF@ となります。これは材料が圧壊されることを意味します。 入力パラメータ ϕ , c , p b , α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHvpGzca GGSaGaaeiiaiaadogacaGGSaGaaeiiaiaadchadaWgaaWcbaGaamOy aaqabaGccaGGSaGaaeiiaiabeg7aHbaa@40B8@ を、Drücker–Prager降伏曲面用に特定する必要があります。これらのパラメータをフィッティングさせるには、少なくとも4つの試験が必要です。最も簡単なケースでは、単軸引張と単軸圧縮を使用して、線形部分 ϕ , and c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHvpGzca GGSaGaaeiiaiaabggacaqGUbGaaeizaiaabccacaWGJbaaaa@3DC0@ を特定できます。 p b , and α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadkgaaeqaaOGaaiilaiaabccacaqGHbGaaeOBaiaabsga caqGGaGaeqySdegaaa@3EC1@ を特定するには、2軸圧縮試験と圧縮 / 圧縮試験が必要です(RD-E: 4701 Kupfer試験でのコンクリートの検証のCC00およびCC01 )。 図 23. さまざまな荷重条件を示すLAW81の降伏曲面 金属など、ほとんどの材料では、塑性ひずみの増分は降伏曲面に垂直と見なすことができます。ただし、降伏曲面に垂直な塑性ひずみの増分が岩石やコンクリートの材料に使用された場合、塑性体積膨張が過大に見積もられます。したがって、非関連塑性流れ則がこれらの材料で使用されます。LAW81では、塑性流れ関数 G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ は次のように定義されます: G = q − p ⋅ tan ψ = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamyCaiabgkHiTiaadchacqGHflY1ciGG0bGaaiyyaiaac6ga cqaHipqEcqGH9aqpcaaIWaaaaa@43B1@ 、右記の場合; p ≤ p a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey izImQaamiCamaaBaaaleaacaWGHbaabeaaaaa@3B0F@ G = q − tan ψ ( p − ( p − p a ) 2 2 ( p 0 − p a ) ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamyCaiabgkHiTiGacshacaGGHbGaaiOBaiabeI8a5naabmaa baGaamiCaiabgkHiTmaalaaabaWaaeWaaeaacaWGWbGaeyOeI0Iaam iCamaaBaaaleaacaWGHbaabeaaaOGaayjkaiaawMcaamaaCaaaleqa baGaaGOmaaaaaOqaaiaaikdadaqadaqaaiaadchadaWgaaWcbaGaaG imaaqabaGccqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGccaGL OaGaayzkaaaaaaGaayjkaiaawMcaaiabg2da9iaaicdaaaa@5184@ 、右記の場合; p a < p ≤ p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadggaaeqaaOGaeyipaWJaamiCaiabgsMiJkaadchadaWg aaWcbaGaaGimaaqabaaaaa@3DF8@ G = F MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamOraaaa@38FB@ 、右記の場合; p > p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey Opa4JaamiCamaaBaaaleaacaaIWaaabeaaaaa@3A36@ 圧力は p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ であるため、降伏関数 F MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ と塑性流れ関数 G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ は同じであり、次の条件が満たされます:(14) G ( p 0 ) = F ( p 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaai ikaiaadchadaWgaaWcbaGaaGimaaqabaGccaGGPaGaeyypa0JaamOr aiaacIcacaWGWbWaaSbaaSqaaiaaicdaaeqaaOGaaiykaaaa@3F77@ (15) ∂G ∂p | p 0 = ∂F ∂p | p 0 =0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kaadEeaaeaacqGHciITcaWGWbaaamaaeeaabaWaaSbaaSqa aiaadchadaWgaaadbaGaaGimaaqabaaaleqaaaGccaGLhWoacqGH9a qpdaWcaaqaaiabgkGi2kaadAeaaeaacqGHciITcaWGWbaaamaaeeaa baWaaSbaaSqaaiaadchadaWgaaadbaGaaGimaaqabaaaleqaaaGcca GLhWoacqGH9aqpcaaIWaaaaa@49BF@ 圧力 p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ は、 ∂ F ∂ p | p 0 = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kaadAeaaeaacqGHciITcaWGWbaaamaaeeaabaWaaSbaaSqa aiaadchadaWgaaadbaGaaGimaaqabaaaleqaaaGccaGLhWoacqGH9a qpcaaIWaaaaa@406B@ である降伏曲面を使用して計算できます。ここで G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ は次のように定義されます:(16) G = q − tan ψ ( p − ( p − p a ) 2 2 ( p 0 − p a ) ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamyCaiabgkHiTiGacshacaGGHbGaaiOBaiabeI8a5naabmaa baGaamiCaiabgkHiTmaalaaabaWaaeWaaeaacaWGWbGaeyOeI0Iaam iCamaaBaaaleaacaWGHbaabeaaaOGaayjkaiaawMcaamaaCaaaleqa baGaaGOmaaaaaOqaaiaaikdadaqadaqaaiaadchadaWgaaWcbaGaaG imaaqabaGccqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGccaGL OaGaayzkaaaaaaGaayjkaiaawMcaaiabg2da9iaaicdaaaa@5184@ パラメータ ψ は、関数内の圧力 p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ でvon Mises応力を使用することで特定できます。 図 24. 塑性流れによるLAW81の降伏曲面 1 Han, D. J., and Wai-Fah Chen."A nonuniform hardening plasticity model for concrete materials." Mechanics of materials 4, no. 3-4 (1985): 283-302
コンクリートおよび岩石材料 コンクリート材料(/MAT/LAW24) 鉄筋コンクリート材料をモデル化するには、降伏におけるcapの有無によらず、LAW24でDrücker-Prager基準を使用します。この材料則では、コンクリート材料の破壊メカニズムとして引張亀裂と圧縮破砕の2つを想定しています。 コンクリートの引張挙動 LAW24では、引張時に、オプションHt、Dsup、および ε max を使用して、引張亀裂と引張破壊を表すことができます。 図 1. LAW24引張荷重 初期の非常に小さな弾性相においては、材料は弾性係数Ecを有します。 引張強度ftに達すると、コンクリートはHtの勾配で軟化し始めます。最大損傷係数Dsupは、亀裂中および亀裂後の残留剛性のモデル化を可能にするため重要です。 図 2. 最大損傷係数の影響 残留剛性は次のように計算されます:(1) E=( 1− D sup )⋅ E c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGfbGaey ypa0ZaaeWaaeaacaaIXaGaeyOeI0IaamiramaaBaaaleaaciGGZbGa aiyDaiaacchaaeqaaaGccaGLOaGaayzkaaGaeyyXICTaamyramaaBa aaleaacaWGJbaabeaaaaa@436C@ 亀裂閉口が生じると、コンクリートは再度弾性となり、(各方向の)損傷係数は維持されます。 引張におけるコンクリートの支持力は、圧縮における支持力よりはるかに小さくなります。引張では、通常これは弾性と見なされます。 損傷の端における現在の剛性を最小化し、それによって引張における残留応力を回避するため、1に近いDsup値(デフォルトでは0.99999)を選択することをお勧めします。 残留応力は、引張による要素の変形が非常に大きい場合、かなり大きくなる場合があります。これは、損傷の原因になった力が残存している場合に発生します。 繊維によって補強されたコンクリートの挙動をシミュレートし、フィッティングするには、Dsup(およびHt)を調整することができます。全破壊ひずみ ε max に達すると、コンクリート材料は破壊します。 圧縮におけるコンクリートの降伏曲面 コンクリートの場合、降伏曲面は、破壊曲面 r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbWaaS baaSqaaiaadAgaaeqaaaaa@386C@ と降伏曲面の間である塑性硬化ゾーンの始まりです。 降伏曲面は、引張ゾーンでの破壊曲面と同じと見なされます。圧縮では、降伏曲面が係数 k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaaaa@3E53@ を使用して破壊曲面にスケールダウンされます。コンクリートのLAW24での降伏は、以下のとおりです:(2) f = r ︸ J 2 p a r t − k ( σ m , k 0 ) ⋅ r f ︸ I 1 p a r t = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbGaey ypa0ZaaGbaaeaacaWGYbaalqaabeqaaiaadQeadaWgaaadbaGaaGOm aaqabaaaleaacaWGWbGaamyyaiaadkhacaWG0baaaOGaayjo+dGaey OeI0YaaGbaaeaaciGGRbWaaeWaaeaacqaHdpWCdaWgaaWcbaGaamyB aaqabaGccaGGSaGaam4AamaaBaaaleaacaaIWaaabeaaaOGaayjkai aawMcaaiabgwSixlaadkhadaWgaaWcbaGaamOzaaqabaaabaGaamys amaaBaaameaacaaIXaaabeaaluaabeqabeaaaeaaaaGaamiCaiaadg gacaWGYbGaamiDaaGccaGL44pacqGH9aqpcaaIWaaaaa@5761@ Icap =0または1(降伏におけるcapなし)の場合、降伏曲線は以下のようになります: 図 3. 降伏におけるcapなしでのDrücker-Prager基準 Icap =2(降伏におけるcapあり)の場合、降伏は以下のようになります: 図 4. 降伏におけるcapありでのDrücker-Prager基準 r < k ( σ m , k 0 ) ⋅ r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey ipaWJaci4AamaabmaabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGa aiilaiaadUgadaWgaaWcbaGaaGimaaqabaaakiaawIcacaGLPaaacq GHflY1caWGYbWaaSbaaSqaaiaadAgaaeqaaaaa@44A6@ (図 4の緑色の領域) 材料は弾性相に属し、降伏には達していません。 r ≥ r f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey yzImRaamOCamaaBaaaleaacaWGMbaabeaaaaa@3B2A@ (図 4の赤色の領域) 材料は破壊されています。 k ( σ m , k 0 ) ⋅ r f < r < r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabgwSixlaadkhada WgaaWcbaGaamOzaaqabaGccqGH8aapcaWGYbGaeyipaWJaamOCamaa BaaaleaacaWGMbaabeaaaaa@47C2@ (図 4の黄色の領域) 材料は、降伏曲面より上で破壊曲面より下の、塑性硬化相に属しています。 入力パラメータ ρ t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaamiDaaqabaaaaa@3943@ は単軸引張試験における破壊静水圧、 ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaamiDaaqabaaaaa@3943@ は単軸圧縮試験における破壊時の静水圧です。 スケールファクター k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaaaa@3E53@ は、平均応力 σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaaaaa@393F@ の関数であり、以下のように表すことができます: σ m ≥ ρ t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaGccqGHLjYScqaHbpGCdaWgaaWcbaGaamiD aaqabaaaaa@3DF4@ (引張)の場合、スケールファクターは k ( σ m , k 0 ) = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaigdaaa a@4014@ です。この場合、降伏曲面は破壊曲面と等しくなります: r= r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey ypa0JaamOCamaaBaaaleaacaWGMbaabeaaaaa@3A69@ 図 5. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ (引張ゾーンにおける) 引張-圧縮領域において、 ρ t > σ m ≥ ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaamiDaaqabaGccqGH+aGpcqaHdpWCdaWgaaWcbaGaamyB aaqabaGccqGHLjYScqaHbpGCdaWgaaWcbaGaam4yaaqabaaaaa@41DA@ の場合、 k ( σ m , k 0 ) = 1 + ( 1 − k 0 ) ⋅ [ ρ t ( 2 ρ c − ρ t ) − 2 ρ c σ m + σ m 2 ] ( ρ c − ρ t ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaigdacq GHRaWkdaWcaaqaamaabmaabaGaaGymaiabgkHiTiaadUgadaWgaaWc baGaaGimaaqabaaakiaawIcacaGLPaaacqGHflY1daWadaqaaiabeg 8aYnaaBaaaleaacaWG0baabeaakmaabmaabaGaaGOmaiabeg8aYnaa BaaaleaacaWGJbaabeaakiabgkHiTiabeg8aYnaaBaaaleaacaWG0b aabeaaaOGaayjkaiaawMcaaiabgkHiTiaaikdacqaHbpGCdaWgaaWc baGaam4yaaqabaGccqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGHRa WkcqaHdpWCdaWgaaWcbaGaamyBaaqabaGcdaahaaWcbeqaaiaaikda aaaakiaawUfacaGLDbaaaeaadaqadaqaaiabeg8aYnaaBaaaleaaca WGJbaabeaakiabgkHiTiabeg8aYnaaBaaaleaacaWG0baabeaaaOGa ayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaaaaaa@6B9F@ ここで、 k y ≤ k 0 ≤ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaOGaeyizImQaam4AamaaBaaaleaacaaIWaaa beaakiabgsMiJkaaigdaaaa@3E87@ 図 6. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 圧縮-引張混合ゾーンでの関数 曲線の残りは、Icapオプションに依存し、異なるスケールファクター k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaaaa@3E53@ が使用されます。 Icap =0または1、かつ σ m < ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaGccqGH8aapcqaHbpGCdaWgaaWcbaGaam4y aaqabaaaaa@3D21@ (圧縮)の場合、 k ( σ m , k 0 ) = k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaadUgada WgaaWcbaGaamyEaaqabaaaaa@4173@ 図 7. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 圧縮ゾーンでの関数 Icap =2(降伏におけるcapあり)、かつ ρ c < σ m < f k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaam4yaaqabaGccqGH8aapcqaHdpWCdaWgaaWcbaGaamyB aaqabaGccqGH8aapcaWGMbWaaSbaaSqaaiaadUgaaeqaaaaa@4036@ (圧縮)の場合、 k ( σ m , k 0 ) = k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaadUgada WgaaWcbaGaamyEaaqabaaaaa@4173@ 図 8. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ capなしのDrücker-Prager基準の関数 f k < σ m < f 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadUgaaeqaaOGaeyipaWJaeq4Wdm3aaSbaaSqaaiaad2ga aeqaaOGaeyipaWJaamOzamaaBaaaleaacaaIWaaabeaaaaa@3F33@ (capゾーン内)において、 k ( σ m , k 0 ) = k 0 [ 1 − ( σ m − f k f 0 − f k ) 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaadUgada WgaaWcbaGaaGimaaqabaGcdaWadaqaaiaaigdacqGHsisldaqadaqa amaalaaabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaeyOeI0Iaam OzamaaBaaaleaacaWGRbaabeaaaOqaaiaadAgadaWgaaWcbaGaaGim aaqabaGccqGHsislcaWGMbWaaSbaaSqaaiaadUgaaeqaaaaaaOGaay jkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2faaaaa @5221@ ここで、 0 ≤ k 0 ≤ k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaGaey izImQaam4AamaaBaaaleaacaaIWaaabeaakiabgsMiJkaadUgadaWg aaWcbaGaamyEaaqabaaaaa@3E7C@ 図 9. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ capありのDrücker-Prager基準の関数 材料定数 k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaaaa@3878@ は、 0 ≤ k y ≤ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaGaey izImQaam4AamaaBaaaleaacaWG5baabeaakiabgsMiJkaaigdaaaa@3D61@ である必要があります。大きな値の k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaaaa@3878@ では、降伏曲面がより高くなります。 例えばIcap =2(capのある降伏)の場合、 k y = 0.8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaOGaeyypa0JaaGimaiaac6cacaaI4aaaaa@3BB6@ と k y = 0.6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaOGaeyypa0JaaGimaiaac6cacaaI2aaaaa@3BB4@ の降伏曲面の違い(図 10)。LAW24における k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaaaa@3878@ のデフォルト値は0.5です。 図 10. 異なる k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 関数値の影響 図 11. 異なる k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 関数値によるDrücker-Prager基準 圧縮におけるコンクリートの塑性流れ則 非関連塑性流れ則はLAW24で使用されます。塑性流れ則は以下のとおりです:(3) g=α I 1 + J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGNbGaey ypa0JaeqySdeMaamysamaaBaaaleaacaaIXaaabeaakiabgUcaRmaa kaaabaGaamOsamaaBaaaleaacaaIYaaabeaaaeqaaaaa@3E57@ ここで、 α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ 塑性域のダイラタンシー。 α = ∂ g ∂ I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpdaWcaaqaaiabgkGi2kaadEgaaeaacqGHciITcaWGjbWaaSba aSqaaiaaigdaaeqaaaaaaaa@3E80@ 体積塑性流れを制御します。 I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaaigdaaeqaaaaa@3813@ 第1応力不変量(静水圧)。 実験に基づいて、 α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ は、 k 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaaaa@3834@ の線形関数です:(4) α = ( 1 − k 0 ) α y + ( k 0 − K y ) α f 1 − K y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpdaWcaaqaamaabmaabaGaaGymaiabgkHiTiaadUgadaWgaaWc baGaaGimaaqabaaakiaawIcacaGLPaaacqaHXoqydaWgaaWcbaGaam yEaaqabaGccqGHRaWkdaqadaqaaiaadUgadaWgaaWcbaGaaGimaaqa baGccqGHsislcaWGlbWaaSbaaSqaaiaadMhaaeqaaaGccaGLOaGaay zkaaGaeqySde2aaSbaaSqaaiaadAgaaeqaaaGcbaGaaGymaiabgkHi TiaadUeadaWgaaWcbaGaamyEaaqabaaaaaaa@4E95@ 次の場合; k 0 = K y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaOGaeyypa0Jaam4samaaBaaaleaacaWG5baa beaaaaa@3B3E@ α = α y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpcqaHXoqydaWgaaWcbaGaamyEaaqabaaaaa@3BCC@ となり、材料が降伏していることを意味します。 次の場合; k 0 < K y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaOGaeyipaWJaam4samaaBaaaleaacaWG5baa beaaaaa@3B3C@ α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ は、cap領域で負となります。 次の場合; k 0 = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaOGaeyypa0JaaGymaaaa@39FF@ α = α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpcqaHXoqydaWgaaWcbaGaamOzaaqabaaaaa@3BB9@ となり、材料が破壊されていることを意味します。 α y , α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyEaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3D3A@ の値は、降伏点を超え、破壊前の材料を表すために使用されます。LAW24では、 α y , α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyEaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3D3A@ に-0.2および-0.1を使用することをお勧めします。 α y , α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyEaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3D3A@ に非常に小さな値が使用されると、体積塑性はなくなります(cap領域なし)。 圧縮におけるコンクリートの圧壊 破壊サーフェスは次のように与えられます: (5) f=r− r f ( σ m ,θ)=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2 da9iaadkhacqGHsislcaWGYbWaaSbaaSqaaiaadAgaaeqaaOGaaiik aiabeo8aZnaaBaaaleaacaWGTbaabeaakiaacYcacqaH4oqCcaGGPa Gaeyypa0JaaGimaaaa@444D@ ここで、 r = 2 J 2 / f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaadQeadaWgaaWcbaGaaGOmaaqabaaabeaa kiaac+cacaWGMbWaaSbaaSqaaiaadogaaeqaaaaa@3D32@ , σ m = I 1 / 3 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaamysamaaBaaaleaacaaIXaaa beaakiaac+cacaaIZaGaamOzamaaBaaaleaacaWGJbaabeaaaaa@3F15@ と θ はLoad角で、次のようになります:(6) cos3θ= J 3 2 ( 3 J 2 ) 3/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaaG4maiabeI7aXjabg2da9maalaaabaGaamOsamaaBaaa leaacaaIZaaabeaaaOqaaiaaikdaaaWaaeWaaeaadaWcaaqaaiaaio daaeaacaWGkbWaaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaawMca amaaCaaaleqabaGaaG4maiaac+cacaaIYaaaaaaa@4540@ このサーフェスを構築するためにOttosenサーフェスが作成されます: (7) r f ( σ m ,θ)= 1 a ( −b+ b 2 −a( σ m −c ) ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaBa aaleaacaWGMbaabeaakiaacIcacqaHdpWCdaWgaaWcbaGaamyBaaqa baGccaGGSaGaeqiUdeNaaiykaiabg2da9maalaaabaGaaGymaaqaai aadggaaaWaaeWaaeaacqGHsislcaWGIbGaey4kaSYaaOaaaeaacaWG IbWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaamyyamaabmaabaGaeq 4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaeyOeI0Iaam4yaaGaayjkaiaa wMcaaaWcbeaaaOGaayjkaiaawMcaaaaa@4FC9@ ここで、 a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaaaa@36DC@ 、 b c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGJbaabeaaaaa@37F1@ 、 b t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGJbaabeaaaaa@37F1@ および c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yaaaa@36DE@ がサーフェスを形成する4つの値で、 (8) b ( b c , b t , θ ) = 1 2 [ b c ( 1 − cos 3 θ ) + b t ( 1 + cos 3 θ ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaabm aabaGaamOyamaaBaaaleaacaWGJbaabeaakiaacYcacaWGIbWaaSba aSqaaiaadshaaeqaaOGaaiilaiabeI7aXbGaayjkaiaawMcaaiabg2 da9maalaaabaGaaGymaaqaaiaaikdaaaWaamWaaeaacaWGIbWaaSba aSqaaiaadogaaeqaaOWaaeWaaeaacaaIXaGaeyOeI0Iaci4yaiaac+ gacaGGZbGaaG4maiabeI7aXbGaayjkaiaawMcaaiabgUcaRiaadkga daWgaaWcbaGaamiDaaqabaGcdaqadaqaaiaaigdacqGHRaWkciGGJb Gaai4BaiaacohacaaIZaGaeqiUdehacaGLOaGaayzkaaaacaGLBbGa ayzxaaaaaa@59F6@ コンクリートの場合、圧縮破壊曲線 r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbWaaS baaSqaaiaadAgaaeqaaaaa@386C@ は、以下の強度で定義できます。 f t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaaaa@386E@ 単軸引張(軸性は1/3) f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaaaa@386E@ 単軸圧縮(軸性は-1/3) f b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaaaa@386E@ 2軸圧縮(軸性は-2/3) f 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAgadaWgaaWcbaGaaGOmaaqabaaaaa@3B28@ 拘束圧縮強度(3軸試験) s 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadohadaWgaaWcbaGaaGimaaqabaaaaa@3B33@ 拘束圧 3D破壊エンベロープをすべて特定する最善の方法は、 f c , f t , f b , f 2 , s 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAgadaWgaaWcbaGaam4yaaqabaGccaGGSaGaamOzamaaBaaa leaacaWG0baabeaakiaacYcacaWGMbWaaSbaaSqaaiaadkgaaeqaaO GaaiilaiaadAgadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaam4Camaa BaaaleaacaaIWaaabeaaaaa@45FB@ のすべての値の実験データを取得する方法です。これを図 12に図式的に示します。 図 12. 3D破壊エンベロープをすべて特定する破壊パラメータ 表 1. 4つの実験からの入力 荷重タイプ サーフェスポイント デフォルト入力 基準 r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@36ED@ 圧力 σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaaaa@38D7@ Lode角 θ 圧縮 ( f c , 0 , 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaai aadAgadaWgaaWcbaGaam4yaaqabaGccaGGSaGaaGimaiaacYcacaaI WaaacaGLOaGaayzkaaaaaa@3DCE@ 必須 r= 2/3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaaaa@3A3A@ σ m =−1/3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaeyOeI0IaaGymaiaac+cacaaI Zaaaaa@3CFF@ cosθ=−1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaeyOeI0IaaGymaaaa@3D2D@ 直接引っ張り ( f t , 0 , 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaai aadAgadaWgaaWcbaGaam4yaaqabaGccaGGSaGaaGimaiaacYcacaaI WaaacaGLOaGaayzkaaaaaa@3DCE@ f t =0 .1 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaOGaaeypaiaabcdacaqGUaGaaeymaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E59@ r= 2/3 ( f t f c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaOWaaeWaaeaadaWc aaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMbWaaSbaaS qaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaaaa@4000@ σ m =1/3( f t f c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaaGymaiaac+cacaaIZaWaaeWa aeaadaWcaaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMb WaaSbaaSqaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaaaa@41CE@ cosθ=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaaGymaaaa@3C40@ 2軸圧縮 ( f 2 , s 0 , s 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaai aadAgadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaam4CamaaBaaaleaa caaIWaaabeaakiaacYcacaWGZbWaaSbaaSqaaiaaicdaaeqaaaGcca GLOaGaayzkaaaaaa@3FFE@ Icap = 1であれば、 f 2 =4 .0 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaaikdaaeqaaOGaaeypaiaabsdacaqGUaGaaeimaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E1F@ Icap = 2であれば、 f 2 =7 .0 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaaikdaaeqaaOGaaeypaiaabsdacaqGUaGaaeimaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E1F@ s 0 =1.25 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGZbWaaS baaSqaaiaaicdaaeqaaOGaaeypaiaabgdacaqGUaGaaeOmaiaabwda caWGMbWaaSbaaSqaaiaadogaaeqaaaaa@3EE1@ r= 2/3 ( f t f c ) σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaOWaaeWaaeaadaWc aaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMbWaaSbaaS qaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaiabeo8aZnaaBaaaleaa caWGTbaabeaaaaa@42E1@ σ m = 2 / 3 ( f t f c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaaGymaiaac+cacaaIZaWaaeWa aeaadaWcaaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMb WaaSbaaSqaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaaaa@41CE@ cos θ = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaaGymaaaa@3C40@ 拘束圧力の下での圧縮強度 ( f b , f b , 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeGabaaUfmaabm aabaGaamOzamaaBaaaleaacaWGIbaabeaakiaacYcacaWGMbWaaSba aSqaaiaadkgaaeqaaOGaaiilaiaaicdaaiaawIcacaGLPaaaaaa@3FDB@ f b =1.2 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadkgaaeqaaOGaaeypaiaabgdacaqGUaGaaeOmaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E49@ r= 2/3 f 2 − s 0 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaOWaaSaaaeaacaWG MbWaaSbaaSqaaiaaikdaaeqaaOGaeyOeI0Iaam4CamaaBaaaleaaca aIWaaabeaaaOqaaiaadAgadaWgaaWcbaGaam4yaaqabaaaaaaa@4105@ σ m = f 2 +2 s 0 3 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0ZaaSaaaeaacaWGMbWaaSbaaSqa aiaaikdaaeqaaOGaey4kaSIaaGOmaiaadohadaWgaaWcbaGaaGimaa qabaaakeaacaaIZaGaamOzamaaBaaaleaacaWGJbaabeaaaaaaaa@4216@ cos θ = − 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaeyOeI0IaaGymaaaa@3D2D@ 図 13 と図 14は、破壊サーフェスを決定するポイントを示しています。 図 13. 平坦な応力面を有する破壊サーフェスのトレース 図 14. 静水圧軸に垂直な複数の断面を有する破壊トレース これらのプロットから、破壊エンベロープが凸型サーフェスではないことがわかります。 図 15 はこの挙動を示しています。 図 15. 2軸圧縮強度値の影響: 作用点以外の、特性に影響するすべての破壊点を固定した状態 図 16. 圧縮強度値の影響: 作用点以外の、特性に影響するすべての破壊点を固定した状態 図 17. 引張強度値の影響: 作用点以外の、特性に影響するすべての破壊点を固定した状態 この特定のケースにおいては、圧縮強度は変化していますが、 f t f c , f b f c , f 2 f c , s 0 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGaaeaaca WGMbWaaSbaaSqaaiaadshaaeqaaaGcbaGaamOzamaaBaaaleaacaWG JbaabeaaaaGccaGGSaGaaeiiamaaliaabaGaamOzamaaBaaaleaaca WGIbaabeaaaOqaaiaadAgadaWgaaWcbaGaam4yaaqabaaaaOGaaiil aiaabccadaWccaqaaiaadAgadaWgaaWcbaGaaGOmaaqabaaakeaaca WGMbWaaSbaaSqaaiaadogaaeqaaaaakiaabYcacaqGGaWaaSGaaeaa caWGZbWaaSbaaSqaaiaaicdaaeqaaaGcbaGaamOzamaaBaaaleaaca WGJbaabeaaaaaaaa@4A37@ といったその他すべての比率は固定されています。これにより、図 18のようなエンベロープスケーリングが生じます。 図 18. 圧縮強度値の影響. 他のすべての比率は固定。 ここでは、LAW24と同じ強度を使用していますが、拘束圧縮強度 f 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaaikdaaeqaaaaa@393B@ には異なる値を使用しています。 図 19. 3軸破壊点 ( σ 1 , σ 2 , σ 3 ) = ( f 2 , s 0 , s 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaamaabmaabaGaeq4Wdm3aaSbaaSqaaiaaigdaaeqaaOGaaiilaiab eo8aZnaaBaaaleaacaaIYaaabeaakiaacYcacqaHdpWCdaWgaaWcba GaaG4maaqabaaakiaawIcacaGLPaaacqGH9aqpdaqadaqaaiaadAga daWgaaWcbaGaaGOmaaqabaGccaGGSaGaam4CamaaBaaaleaacaaIWa aabeaakiaacYcacaWGZbWaaSbaaSqaaiaaicdaaeqaaaGccaGLOaGa ayzkaaaaaa@4DF9@ の影響を受ける平坦な応力面上の破壊エンベロープ f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadogaaeqaaaaa@385D@ 、およびコンクリート破壊の定義に使用する r − σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey OeI0Iaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaaaa@3B23@ 空間での比率 f t f c , and f b f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWccaqaai aadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMbWaaSbaaSqaaiaa dogaaeqaaaaakiaacYcacaqGGaGaaeyyaiaab6gacaqGKbGaaeiiam aaliaabaGaamOzamaaBaaaleaacaWGIbaabeaaaOqaaiaadAgadaWg aaWcbaGaam4yaaqabaaaaaaa@435E@ は次のようになります: 図 20. 破壊曲線を決定するための各種試験(単軸引張、単軸圧縮、および2軸圧縮) ここで、破壊曲線は、 r = 2 J 2 = 2 3 σ V M MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey ypa0ZaaOaaaeaacaaIYaGaamOsamaaBaaaleaacaaIYaaabeaaaeqa aOGaeyypa0ZaaOaaaeaadaWcaaqaaiaaikdaaeaacaaIZaaaaaWcbe aakiabeo8aZnaaBaaaleaacaWGwbGaamytaaqabaaaaa@4138@ を使用して定義され、 σ m = I 1 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaGccqGH9aqpdaWcaaqaaiaadMeadaWgaaWc baGaaGymaaqabaaakeaacaaIZaaaaaaa@3CDB@ は平均応力(圧力)、 I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaaigdaaeqaaaaa@3813@ および J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaaigdaaeqaaaaa@3813@ は第1および第2応力不変量です。 破壊曲線 r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbWaaS baaSqaaiaadAgaaeqaaaaa@386C@ に達すると、材料は破壊します。 コンクリートの補強Radiossでは、2つの方法でコンクリートの補強をシミュレートできます。 1つは、ビームまたはトラス要素を複数の運動条件でコンクリートに結合する方法です。 もう1つは、LAW24のパラメータを直交異方性ソリッドプロパティ/PROP/TYPE6とともに使用し、補強方向を定義する方法です。LAW24のパラメータ α 1 , α 2 , α 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaaGymaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caaIYaaabeaakiaacYcacaqGGaGaeqySde2aaSbaaSqaaiaaiodaae qaaaaa@40AD@ を使用して、方向1、2、3について、全体のコンクリート断面積に対する補強断面積の比率を定義します。(9) α i = A r e a s t e e l A r e a c o n c r e t e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyAaaqabaGccqGH9aqpdaWcaaqaaiaadgeacaWGYbGa amyzaiaadggadaWgaaWcbaGaam4CaiaadshacaWGLbGaamyzaiaadY gaaeqaaaGcbaGaamyqaiaadkhacaWGLbGaamyyamaaBaaaleaacaWG JbGaam4Baiaad6gacaWGJbGaamOCaiaadwgacaWG0bGaamyzaaqaba aaaaaa@4DE4@ ここで、 σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyEaaqabaaaaa@394B@ は、補強の降伏応力です。補強としてスチールが使用される場合は、 σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyEaaqabaaaaa@394B@ がスチールの降伏応力で、 E t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGfbWaaS baaSqaaiaadshaaeqaaaaa@384D@ が塑性相におけるスチールの弾性率です。 図 21. 補強(スチール)の応力-ひずみ曲線 コンクリート材料(/MAT/LAW81) LAW81は岩石またはコンクリート材料のモデル化に使用できます。 Drücker-Prager降伏基準 LAW81ではDrücker-Prager降伏基準を使用します。ここでは、降伏曲面と破壊曲面が同じです。降伏基準は以下のとおりです:(10) F = q ︸ J 2 part − r c ( p ) ⋅ ( p tan ϕ + c ) ︸ I 1 part = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbGaey ypa0ZaaGbaaeaacaWGXbaaleaacaWGkbWaaSbaaWqaaiaaikdaaeqa aSGaaeiiaiaabchacaqGHbGaaeOCaiaabshaaOGaayjo+dGaeyOeI0 YaaGbaaeaaciGGYbWaaSbaaSqaaiaacogaaeqaaOWaaeWaaeaacaWG WbaacaGLOaGaayzkaaGaeyyXIC9aaeWaaeaacaWGWbGaciiDaiaacg gacaGGUbGaeqy1dyMaey4kaSIaam4yaaGaayjkaiaawMcaaaWcbaGa amysamaaBaaameaacaaIXaaabeaaliaabccacaqGWbGaaeyyaiaabk hacaqG0baakiaawIJ=aiabg2da9iaaicdaaaa@5BE0@ ここで、 q MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ 以下の条件におけるvon Mises応力: q = σ V M = 3 J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0Jaeq4Wdm3aaSbaaSqaaiaadAfacaWGnbaabeaakiabg2da9maa kaaabaGaaG4maiaadQeadaWgaaWcbaGaaGOmaaqabaaabeaaaaa@3F8A@ p MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ 圧力は以下のように定義されます: p = 1 3 I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey ypa0ZaaSaaaeaacaaIXaaabaGaaG4maaaacaWGjbWaaSbaaSqaaiaa igdaaeqaaaaa@3B96@ 図 22. 降伏曲面(LAW81) 降伏曲面は2つの部分で表されます: 線形部分( p ≤ p a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey izImQaamiCamaaBaaaleaacaWGHbaabeaaaaa@3B0F@ )、ここではスケール関数が r c ( p ) = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGYbWaaS baaSqaaiaacogaaeqaaOWaaeWaaeaacaWGWbaacaGLOaGaayzkaaGa eyypa0JaaGymaaaa@3CB2@ で、von Mises応力が圧力に線形比例します:(11) q = p tan ϕ + c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0JaamiCaiGacshacaGGHbGaaiOBaiabew9aMjabgUcaRiaadoga aaa@3FB2@ ここで、 c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ 粘度。せん断強度による降伏エンベロープを制限します。 c = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGJbGaey ypa0JaaGimaaaa@3906@ の場合、材料に引張強度はありません。 ϕ 内部摩擦の角度。降伏エンベロープの勾配を定義します。 c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ および ϕ は、Mohr-Coulomb降伏曲面の定義にも使用されます。Drücker-Prage降伏曲面は、Mohr-Coulomb降伏曲面を滑らかにしたものです。 降伏曲面の2つ目の部分( p a < p < p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadggaaeqaaOGaeyipaWJaamiCaiabgYda8iaadchadaWg aaWcbaGaamOyaaqabaaaaa@3D74@ )は、cap制限をシミュレートします。岩石またはコンクリート材料での圧力の増加により、材料の降伏が増加しますが、圧力が十分に大きくなると、岩石またはコンクリート材料は圧壊されます。cap制限のあるDrücker-Pragerモデルを使用して、この挙動をモデル化できます。cap制限はの部分で定義され、以下のスケール関数を使用します:(12) r c ( p ) = 1 − ( p − p a p b − p a ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGYbWaaS baaSqaaiaacogaaeqaaOWaaeWaaeaacaWGWbaacaGLOaGaayzkaaGa eyypa0ZaaOaaaeaacaaIXaGaeyOeI0YaaeWaaeaadaWcaaqaaiaadc hacqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGcbaGaamiCamaa BaaaleaacaWGIbaabeaakiabgkHiTiaadchadaWgaaWcbaGaamyyaa qabaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaqabaaa aa@4934@ von Mises応力は以下のようになります:(13) q = 1 − ( p − p a p b − p a ) 2 ⋅ ( p tan ϕ + c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0ZaaOaaaeaacaaIXaGaeyOeI0YaaeWaaeaadaWcaaqaaiaadcha cqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGcbaGaamiCamaaBa aaleaacaWGIbaabeaakiabgkHiTiaadchadaWgaaWcbaGaamyyaaqa baaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaqabaGccq GHflY1daqadaqaaiaadchaciGG0bGaaiyyaiaac6gacqaHvpGzcqGH RaWkcaWGJbaacaGLOaGaayzkaaaaaa@50CC@ ここで、 p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadkgaaeqaaaaa@3866@ 曲線はfct_IDPb入力を使用して定義されます。 p a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadkgaaeqaaaaa@3866@ 入力 α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ 率の値を使用してRadiossによって計算されます。 p a = α ⋅ p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadggaaeqaaOGaeyypa0JaeqySdeMaeyyXICTaamiCamaa BaaaleaacaWGIbaabeaaaaa@3F66@ ここで、 0 < α < 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaGaey ipaWJaeqySdeMaeyipaWJaaGymaaaa@3B7A@ 。 ここで、 p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ は、降伏曲線の最大ポイントです。ここで、 ∂ F ∂ p ( p 0 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kaadAeaaeaacqGHciITcaWGWbaaamaabmaabaGaamiCamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaicdaaa a@4028@ p = p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey ypa0JaamiCamaaBaaaleaacaWGIbaabeaaaaa@3A61@ の場合、 r c ( p b ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGYbWaaS baaSqaaiaacogaaeqaaOWaaeWaaeaacaWGWbWaaSbaaSqaaiaadkga aeqaaaGccaGLOaGaayzkaaGaeyypa0JaaGimaaaa@3DCE@ となり、降伏関数は、 q = 0 ⋅ ( p tan ϕ + c ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0JaaGimaiabgwSixpaabmaabaGaamiCaiGacshacaGGHbGaaiOB aiabew9aMjabgUcaRiaadogaaiaawIcacaGLPaaacqGH9aqpcaaIWa aaaa@45FF@ となります。これは材料が圧壊されることを意味します。 入力パラメータ ϕ , c , p b , α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHvpGzca GGSaGaaeiiaiaadogacaGGSaGaaeiiaiaadchadaWgaaWcbaGaamOy aaqabaGccaGGSaGaaeiiaiabeg7aHbaa@40B8@ を、Drücker–Prager降伏曲面用に特定する必要があります。これらのパラメータをフィッティングさせるには、少なくとも4つの試験が必要です。最も簡単なケースでは、単軸引張と単軸圧縮を使用して、線形部分 ϕ , and c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHvpGzca GGSaGaaeiiaiaabggacaqGUbGaaeizaiaabccacaWGJbaaaa@3DC0@ を特定できます。 p b , and α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadkgaaeqaaOGaaiilaiaabccacaqGHbGaaeOBaiaabsga caqGGaGaeqySdegaaa@3EC1@ を特定するには、2軸圧縮試験と圧縮 / 圧縮試験が必要です(RD-E: 4701 Kupfer試験でのコンクリートの検証のCC00およびCC01 )。 図 23. さまざまな荷重条件を示すLAW81の降伏曲面 金属など、ほとんどの材料では、塑性ひずみの増分は降伏曲面に垂直と見なすことができます。ただし、降伏曲面に垂直な塑性ひずみの増分が岩石やコンクリートの材料に使用された場合、塑性体積膨張が過大に見積もられます。したがって、非関連塑性流れ則がこれらの材料で使用されます。LAW81では、塑性流れ関数 G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ は次のように定義されます: G = q − p ⋅ tan ψ = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamyCaiabgkHiTiaadchacqGHflY1ciGG0bGaaiyyaiaac6ga cqaHipqEcqGH9aqpcaaIWaaaaa@43B1@ 、右記の場合; p ≤ p a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey izImQaamiCamaaBaaaleaacaWGHbaabeaaaaa@3B0F@ G = q − tan ψ ( p − ( p − p a ) 2 2 ( p 0 − p a ) ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamyCaiabgkHiTiGacshacaGGHbGaaiOBaiabeI8a5naabmaa baGaamiCaiabgkHiTmaalaaabaWaaeWaaeaacaWGWbGaeyOeI0Iaam iCamaaBaaaleaacaWGHbaabeaaaOGaayjkaiaawMcaamaaCaaaleqa baGaaGOmaaaaaOqaaiaaikdadaqadaqaaiaadchadaWgaaWcbaGaaG imaaqabaGccqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGccaGL OaGaayzkaaaaaaGaayjkaiaawMcaaiabg2da9iaaicdaaaa@5184@ 、右記の場合; p a < p ≤ p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadggaaeqaaOGaeyipaWJaamiCaiabgsMiJkaadchadaWg aaWcbaGaaGimaaqabaaaaa@3DF8@ G = F MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamOraaaa@38FB@ 、右記の場合; p > p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey Opa4JaamiCamaaBaaaleaacaaIWaaabeaaaaa@3A36@ 圧力は p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ であるため、降伏関数 F MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ と塑性流れ関数 G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ は同じであり、次の条件が満たされます:(14) G ( p 0 ) = F ( p 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaai ikaiaadchadaWgaaWcbaGaaGimaaqabaGccaGGPaGaeyypa0JaamOr aiaacIcacaWGWbWaaSbaaSqaaiaaicdaaeqaaOGaaiykaaaa@3F77@ (15) ∂G ∂p | p 0 = ∂F ∂p | p 0 =0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kaadEeaaeaacqGHciITcaWGWbaaamaaeeaabaWaaSbaaSqa aiaadchadaWgaaadbaGaaGimaaqabaaaleqaaaGccaGLhWoacqGH9a qpdaWcaaqaaiabgkGi2kaadAeaaeaacqGHciITcaWGWbaaamaaeeaa baWaaSbaaSqaaiaadchadaWgaaadbaGaaGimaaqabaaaleqaaaGcca GLhWoacqGH9aqpcaaIWaaaaa@49BF@ 圧力 p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ は、 ∂ F ∂ p | p 0 = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kaadAeaaeaacqGHciITcaWGWbaaamaaeeaabaWaaSbaaSqa aiaadchadaWgaaadbaGaaGimaaqabaaaleqaaaGccaGLhWoacqGH9a qpcaaIWaaaaa@406B@ である降伏曲面を使用して計算できます。ここで G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ は次のように定義されます:(16) G = q − tan ψ ( p − ( p − p a ) 2 2 ( p 0 − p a ) ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamyCaiabgkHiTiGacshacaGGHbGaaiOBaiabeI8a5naabmaa baGaamiCaiabgkHiTmaalaaabaWaaeWaaeaacaWGWbGaeyOeI0Iaam iCamaaBaaaleaacaWGHbaabeaaaOGaayjkaiaawMcaamaaCaaaleqa baGaaGOmaaaaaOqaaiaaikdadaqadaqaaiaadchadaWgaaWcbaGaaG imaaqabaGccqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGccaGL OaGaayzkaaaaaaGaayjkaiaawMcaaiabg2da9iaaicdaaaa@5184@ パラメータ ψ は、関数内の圧力 p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ でvon Mises応力を使用することで特定できます。 図 24. 塑性流れによるLAW81の降伏曲面
コンクリート材料(/MAT/LAW24) 鉄筋コンクリート材料をモデル化するには、降伏におけるcapの有無によらず、LAW24でDrücker-Prager基準を使用します。この材料則では、コンクリート材料の破壊メカニズムとして引張亀裂と圧縮破砕の2つを想定しています。 コンクリートの引張挙動 LAW24では、引張時に、オプションHt、Dsup、および ε max を使用して、引張亀裂と引張破壊を表すことができます。 図 1. LAW24引張荷重 初期の非常に小さな弾性相においては、材料は弾性係数Ecを有します。 引張強度ftに達すると、コンクリートはHtの勾配で軟化し始めます。最大損傷係数Dsupは、亀裂中および亀裂後の残留剛性のモデル化を可能にするため重要です。 図 2. 最大損傷係数の影響 残留剛性は次のように計算されます:(1) E=( 1− D sup )⋅ E c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGfbGaey ypa0ZaaeWaaeaacaaIXaGaeyOeI0IaamiramaaBaaaleaaciGGZbGa aiyDaiaacchaaeqaaaGccaGLOaGaayzkaaGaeyyXICTaamyramaaBa aaleaacaWGJbaabeaaaaa@436C@ 亀裂閉口が生じると、コンクリートは再度弾性となり、(各方向の)損傷係数は維持されます。 引張におけるコンクリートの支持力は、圧縮における支持力よりはるかに小さくなります。引張では、通常これは弾性と見なされます。 損傷の端における現在の剛性を最小化し、それによって引張における残留応力を回避するため、1に近いDsup値(デフォルトでは0.99999)を選択することをお勧めします。 残留応力は、引張による要素の変形が非常に大きい場合、かなり大きくなる場合があります。これは、損傷の原因になった力が残存している場合に発生します。 繊維によって補強されたコンクリートの挙動をシミュレートし、フィッティングするには、Dsup(およびHt)を調整することができます。全破壊ひずみ ε max に達すると、コンクリート材料は破壊します。 圧縮におけるコンクリートの降伏曲面 コンクリートの場合、降伏曲面は、破壊曲面 r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbWaaS baaSqaaiaadAgaaeqaaaaa@386C@ と降伏曲面の間である塑性硬化ゾーンの始まりです。 降伏曲面は、引張ゾーンでの破壊曲面と同じと見なされます。圧縮では、降伏曲面が係数 k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaaaa@3E53@ を使用して破壊曲面にスケールダウンされます。コンクリートのLAW24での降伏は、以下のとおりです:(2) f = r ︸ J 2 p a r t − k ( σ m , k 0 ) ⋅ r f ︸ I 1 p a r t = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbGaey ypa0ZaaGbaaeaacaWGYbaalqaabeqaaiaadQeadaWgaaadbaGaaGOm aaqabaaaleaacaWGWbGaamyyaiaadkhacaWG0baaaOGaayjo+dGaey OeI0YaaGbaaeaaciGGRbWaaeWaaeaacqaHdpWCdaWgaaWcbaGaamyB aaqabaGccaGGSaGaam4AamaaBaaaleaacaaIWaaabeaaaOGaayjkai aawMcaaiabgwSixlaadkhadaWgaaWcbaGaamOzaaqabaaabaGaamys amaaBaaameaacaaIXaaabeaaluaabeqabeaaaeaaaaGaamiCaiaadg gacaWGYbGaamiDaaGccaGL44pacqGH9aqpcaaIWaaaaa@5761@ Icap =0または1(降伏におけるcapなし)の場合、降伏曲線は以下のようになります: 図 3. 降伏におけるcapなしでのDrücker-Prager基準 Icap =2(降伏におけるcapあり)の場合、降伏は以下のようになります: 図 4. 降伏におけるcapありでのDrücker-Prager基準 r < k ( σ m , k 0 ) ⋅ r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey ipaWJaci4AamaabmaabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGa aiilaiaadUgadaWgaaWcbaGaaGimaaqabaaakiaawIcacaGLPaaacq GHflY1caWGYbWaaSbaaSqaaiaadAgaaeqaaaaa@44A6@ (図 4の緑色の領域) 材料は弾性相に属し、降伏には達していません。 r ≥ r f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey yzImRaamOCamaaBaaaleaacaWGMbaabeaaaaa@3B2A@ (図 4の赤色の領域) 材料は破壊されています。 k ( σ m , k 0 ) ⋅ r f < r < r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabgwSixlaadkhada WgaaWcbaGaamOzaaqabaGccqGH8aapcaWGYbGaeyipaWJaamOCamaa BaaaleaacaWGMbaabeaaaaa@47C2@ (図 4の黄色の領域) 材料は、降伏曲面より上で破壊曲面より下の、塑性硬化相に属しています。 入力パラメータ ρ t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaamiDaaqabaaaaa@3943@ は単軸引張試験における破壊静水圧、 ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaamiDaaqabaaaaa@3943@ は単軸圧縮試験における破壊時の静水圧です。 スケールファクター k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaaaa@3E53@ は、平均応力 σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaaaaa@393F@ の関数であり、以下のように表すことができます: σ m ≥ ρ t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaGccqGHLjYScqaHbpGCdaWgaaWcbaGaamiD aaqabaaaaa@3DF4@ (引張)の場合、スケールファクターは k ( σ m , k 0 ) = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaigdaaa a@4014@ です。この場合、降伏曲面は破壊曲面と等しくなります: r= r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey ypa0JaamOCamaaBaaaleaacaWGMbaabeaaaaa@3A69@ 図 5. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ (引張ゾーンにおける) 引張-圧縮領域において、 ρ t > σ m ≥ ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaamiDaaqabaGccqGH+aGpcqaHdpWCdaWgaaWcbaGaamyB aaqabaGccqGHLjYScqaHbpGCdaWgaaWcbaGaam4yaaqabaaaaa@41DA@ の場合、 k ( σ m , k 0 ) = 1 + ( 1 − k 0 ) ⋅ [ ρ t ( 2 ρ c − ρ t ) − 2 ρ c σ m + σ m 2 ] ( ρ c − ρ t ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaigdacq GHRaWkdaWcaaqaamaabmaabaGaaGymaiabgkHiTiaadUgadaWgaaWc baGaaGimaaqabaaakiaawIcacaGLPaaacqGHflY1daWadaqaaiabeg 8aYnaaBaaaleaacaWG0baabeaakmaabmaabaGaaGOmaiabeg8aYnaa BaaaleaacaWGJbaabeaakiabgkHiTiabeg8aYnaaBaaaleaacaWG0b aabeaaaOGaayjkaiaawMcaaiabgkHiTiaaikdacqaHbpGCdaWgaaWc baGaam4yaaqabaGccqaHdpWCdaWgaaWcbaGaamyBaaqabaGccqGHRa WkcqaHdpWCdaWgaaWcbaGaamyBaaqabaGcdaahaaWcbeqaaiaaikda aaaakiaawUfacaGLDbaaaeaadaqadaqaaiabeg8aYnaaBaaaleaaca WGJbaabeaakiabgkHiTiabeg8aYnaaBaaaleaacaWG0baabeaaaOGa ayjkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaaaaaa@6B9F@ ここで、 k y ≤ k 0 ≤ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaOGaeyizImQaam4AamaaBaaaleaacaaIWaaa beaakiabgsMiJkaaigdaaaa@3E87@ 図 6. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 圧縮-引張混合ゾーンでの関数 曲線の残りは、Icapオプションに依存し、異なるスケールファクター k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaaaa@3E53@ が使用されます。 Icap =0または1、かつ σ m < ρ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaGccqGH8aapcqaHbpGCdaWgaaWcbaGaam4y aaqabaaaaa@3D21@ (圧縮)の場合、 k ( σ m , k 0 ) = k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaadUgada WgaaWcbaGaamyEaaqabaaaaa@4173@ 図 7. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 圧縮ゾーンでの関数 Icap =2(降伏におけるcapあり)、かつ ρ c < σ m < f k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHbpGCda WgaaWcbaGaam4yaaqabaGccqGH8aapcqaHdpWCdaWgaaWcbaGaamyB aaqabaGccqGH8aapcaWGMbWaaSbaaSqaaiaadUgaaeqaaaaa@4036@ (圧縮)の場合、 k ( σ m , k 0 ) = k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaadUgada WgaaWcbaGaamyEaaqabaaaaa@4173@ 図 8. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ capなしのDrücker-Prager基準の関数 f k < σ m < f 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadUgaaeqaaOGaeyipaWJaeq4Wdm3aaSbaaSqaaiaad2ga aeqaaOGaeyipaWJaamOzamaaBaaaleaacaaIWaaabeaaaaa@3F33@ (capゾーン内)において、 k ( σ m , k 0 ) = k 0 [ 1 − ( σ m − f k f 0 − f k ) 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGRbWaae WaaeaacqaHdpWCdaWgaaWcbaGaamyBaaqabaGccaGGSaGaam4Aamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaadUgada WgaaWcbaGaaGimaaqabaGcdaWadaqaaiaaigdacqGHsisldaqadaqa amaalaaabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaeyOeI0Iaam OzamaaBaaaleaacaWGRbaabeaaaOqaaiaadAgadaWgaaWcbaGaaGim aaqabaGccqGHsislcaWGMbWaaSbaaSqaaiaadUgaaeqaaaaaaOGaay jkaiaawMcaamaaCaaaleqabaGaaGOmaaaaaOGaay5waiaaw2faaaaa @5221@ ここで、 0 ≤ k 0 ≤ k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaGaey izImQaam4AamaaBaaaleaacaaIWaaabeaakiabgsMiJkaadUgadaWg aaWcbaGaamyEaaqabaaaaa@3E7C@ 図 9. k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ capありのDrücker-Prager基準の関数 材料定数 k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaaaa@3878@ は、 0 ≤ k y ≤ 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaGaey izImQaam4AamaaBaaaleaacaWG5baabeaakiabgsMiJkaaigdaaaa@3D61@ である必要があります。大きな値の k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaaaa@3878@ では、降伏曲面がより高くなります。 例えばIcap =2(capのある降伏)の場合、 k y = 0.8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaOGaeyypa0JaaGimaiaac6cacaaI4aaaaa@3BB6@ と k y = 0.6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaOGaeyypa0JaaGimaiaac6cacaaI2aaaaa@3BB4@ の降伏曲面の違い(図 10)。LAW24における k y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaadMhaaeqaaaaa@3878@ のデフォルト値は0.5です。 図 10. 異なる k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 関数値の影響 図 11. 異なる k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ 関数値によるDrücker-Prager基準 圧縮におけるコンクリートの塑性流れ則 非関連塑性流れ則はLAW24で使用されます。塑性流れ則は以下のとおりです:(3) g=α I 1 + J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGNbGaey ypa0JaeqySdeMaamysamaaBaaaleaacaaIXaaabeaakiabgUcaRmaa kaaabaGaamOsamaaBaaaleaacaaIYaaabeaaaeqaaaaa@3E57@ ここで、 α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ 塑性域のダイラタンシー。 α = ∂ g ∂ I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpdaWcaaqaaiabgkGi2kaadEgaaeaacqGHciITcaWGjbWaaSba aSqaaiaaigdaaeqaaaaaaaa@3E80@ 体積塑性流れを制御します。 I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaaigdaaeqaaaaa@3813@ 第1応力不変量(静水圧)。 実験に基づいて、 α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ は、 k 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaaaa@3834@ の線形関数です:(4) α = ( 1 − k 0 ) α y + ( k 0 − K y ) α f 1 − K y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpdaWcaaqaamaabmaabaGaaGymaiabgkHiTiaadUgadaWgaaWc baGaaGimaaqabaaakiaawIcacaGLPaaacqaHXoqydaWgaaWcbaGaam yEaaqabaGccqGHRaWkdaqadaqaaiaadUgadaWgaaWcbaGaaGimaaqa baGccqGHsislcaWGlbWaaSbaaSqaaiaadMhaaeqaaaGccaGLOaGaay zkaaGaeqySde2aaSbaaSqaaiaadAgaaeqaaaGcbaGaaGymaiabgkHi TiaadUeadaWgaaWcbaGaamyEaaqabaaaaaaa@4E95@ 次の場合; k 0 = K y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaOGaeyypa0Jaam4samaaBaaaleaacaWG5baa beaaaaa@3B3E@ α = α y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpcqaHXoqydaWgaaWcbaGaamyEaaqabaaaaa@3BCC@ となり、材料が降伏していることを意味します。 次の場合; k 0 < K y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaOGaeyipaWJaam4samaaBaaaleaacaWG5baa beaaaaa@3B3C@ α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ は、cap領域で負となります。 次の場合; k 0 = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGRbWaaS baaSqaaiaaicdaaeqaaOGaeyypa0JaaGymaaaa@39FF@ α = α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqycq GH9aqpcqaHXoqydaWgaaWcbaGaamOzaaqabaaaaa@3BB9@ となり、材料が破壊されていることを意味します。 α y , α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyEaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3D3A@ の値は、降伏点を超え、破壊前の材料を表すために使用されます。LAW24では、 α y , α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyEaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3D3A@ に-0.2および-0.1を使用することをお勧めします。 α y , α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyEaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caWGMbaabeaaaaa@3D3A@ に非常に小さな値が使用されると、体積塑性はなくなります(cap領域なし)。 圧縮におけるコンクリートの圧壊 破壊サーフェスは次のように与えられます: (5) f=r− r f ( σ m ,θ)=0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2 da9iaadkhacqGHsislcaWGYbWaaSbaaSqaaiaadAgaaeqaaOGaaiik aiabeo8aZnaaBaaaleaacaWGTbaabeaakiaacYcacqaH4oqCcaGGPa Gaeyypa0JaaGimaaaa@444D@ ここで、 r = 2 J 2 / f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaadQeadaWgaaWcbaGaaGOmaaqabaaabeaa kiaac+cacaWGMbWaaSbaaSqaaiaadogaaeqaaaaa@3D32@ , σ m = I 1 / 3 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaamysamaaBaaaleaacaaIXaaa beaakiaac+cacaaIZaGaamOzamaaBaaaleaacaWGJbaabeaaaaa@3F15@ と θ はLoad角で、次のようになります:(6) cos3θ= J 3 2 ( 3 J 2 ) 3/2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaaG4maiabeI7aXjabg2da9maalaaabaGaamOsamaaBaaa leaacaaIZaaabeaaaOqaaiaaikdaaaWaaeWaaeaadaWcaaqaaiaaio daaeaacaWGkbWaaSbaaSqaaiaaikdaaeqaaaaaaOGaayjkaiaawMca amaaCaaaleqabaGaaG4maiaac+cacaaIYaaaaaaa@4540@ このサーフェスを構築するためにOttosenサーフェスが作成されます: (7) r f ( σ m ,θ)= 1 a ( −b+ b 2 −a( σ m −c ) ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCamaaBa aaleaacaWGMbaabeaakiaacIcacqaHdpWCdaWgaaWcbaGaamyBaaqa baGccaGGSaGaeqiUdeNaaiykaiabg2da9maalaaabaGaaGymaaqaai aadggaaaWaaeWaaeaacqGHsislcaWGIbGaey4kaSYaaOaaaeaacaWG IbWaaWbaaSqabeaacaaIYaaaaOGaeyOeI0IaamyyamaabmaabaGaeq 4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaeyOeI0Iaam4yaaGaayjkaiaa wMcaaaWcbeaaaOGaayjkaiaawMcaaaaa@4FC9@ ここで、 a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaaaa@36DC@ 、 b c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGJbaabeaaaaa@37F1@ 、 b t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaaBa aaleaacaWGJbaabeaaaaa@37F1@ および c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yaaaa@36DE@ がサーフェスを形成する4つの値で、 (8) b ( b c , b t , θ ) = 1 2 [ b c ( 1 − cos 3 θ ) + b t ( 1 + cos 3 θ ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOyamaabm aabaGaamOyamaaBaaaleaacaWGJbaabeaakiaacYcacaWGIbWaaSba aSqaaiaadshaaeqaaOGaaiilaiabeI7aXbGaayjkaiaawMcaaiabg2 da9maalaaabaGaaGymaaqaaiaaikdaaaWaamWaaeaacaWGIbWaaSba aSqaaiaadogaaeqaaOWaaeWaaeaacaaIXaGaeyOeI0Iaci4yaiaac+ gacaGGZbGaaG4maiabeI7aXbGaayjkaiaawMcaaiabgUcaRiaadkga daWgaaWcbaGaamiDaaqabaGcdaqadaqaaiaaigdacqGHRaWkciGGJb Gaai4BaiaacohacaaIZaGaeqiUdehacaGLOaGaayzkaaaacaGLBbGa ayzxaaaaaa@59F6@ コンクリートの場合、圧縮破壊曲線 r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbWaaS baaSqaaiaadAgaaeqaaaaa@386C@ は、以下の強度で定義できます。 f t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaaaa@386E@ 単軸引張(軸性は1/3) f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaaaa@386E@ 単軸圧縮(軸性は-1/3) f b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaaaa@386E@ 2軸圧縮(軸性は-2/3) f 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAgadaWgaaWcbaGaaGOmaaqabaaaaa@3B28@ 拘束圧縮強度(3軸試験) s 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadohadaWgaaWcbaGaaGimaaqabaaaaa@3B33@ 拘束圧 3D破壊エンベロープをすべて特定する最善の方法は、 f c , f t , f b , f 2 , s 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAgadaWgaaWcbaGaam4yaaqabaGccaGGSaGaamOzamaaBaaa leaacaWG0baabeaakiaacYcacaWGMbWaaSbaaSqaaiaadkgaaeqaaO GaaiilaiaadAgadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaam4Camaa BaaaleaacaaIWaaabeaaaaa@45FB@ のすべての値の実験データを取得する方法です。これを図 12に図式的に示します。 図 12. 3D破壊エンベロープをすべて特定する破壊パラメータ 表 1. 4つの実験からの入力 荷重タイプ サーフェスポイント デフォルト入力 基準 r MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@36ED@ 圧力 σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaaaa@38D7@ Lode角 θ 圧縮 ( f c , 0 , 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaai aadAgadaWgaaWcbaGaam4yaaqabaGccaGGSaGaaGimaiaacYcacaaI WaaacaGLOaGaayzkaaaaaa@3DCE@ 必須 r= 2/3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaaaa@3A3A@ σ m =−1/3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaeyOeI0IaaGymaiaac+cacaaI Zaaaaa@3CFF@ cosθ=−1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaeyOeI0IaaGymaaaa@3D2D@ 直接引っ張り ( f t , 0 , 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaai aadAgadaWgaaWcbaGaam4yaaqabaGccaGGSaGaaGimaiaacYcacaaI WaaacaGLOaGaayzkaaaaaa@3DCE@ f t =0 .1 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadshaaeqaaOGaaeypaiaabcdacaqGUaGaaeymaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E59@ r= 2/3 ( f t f c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaOWaaeWaaeaadaWc aaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMbWaaSbaaS qaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaaaa@4000@ σ m =1/3( f t f c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaaGymaiaac+cacaaIZaWaaeWa aeaadaWcaaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMb WaaSbaaSqaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaaaa@41CE@ cosθ=1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaaGymaaaa@3C40@ 2軸圧縮 ( f 2 , s 0 , s 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaqadaqaai aadAgadaWgaaWcbaGaaGOmaaqabaGccaGGSaGaam4CamaaBaaaleaa caaIWaaabeaakiaacYcacaWGZbWaaSbaaSqaaiaaicdaaeqaaaGcca GLOaGaayzkaaaaaa@3FFE@ Icap = 1であれば、 f 2 =4 .0 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaaikdaaeqaaOGaaeypaiaabsdacaqGUaGaaeimaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E1F@ Icap = 2であれば、 f 2 =7 .0 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaaikdaaeqaaOGaaeypaiaabsdacaqGUaGaaeimaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E1F@ s 0 =1.25 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGZbWaaS baaSqaaiaaicdaaeqaaOGaaeypaiaabgdacaqGUaGaaeOmaiaabwda caWGMbWaaSbaaSqaaiaadogaaeqaaaaa@3EE1@ r= 2/3 ( f t f c ) σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaOWaaeWaaeaadaWc aaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMbWaaSbaaS qaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaiabeo8aZnaaBaaaleaa caWGTbaabeaaaaa@42E1@ σ m = 2 / 3 ( f t f c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0JaaGymaiaac+cacaaIZaWaaeWa aeaadaWcaaqaaiaadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMb WaaSbaaSqaaiaadogaaeqaaaaaaOGaayjkaiaawMcaaaaa@41CE@ cos θ = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaaGymaaaa@3C40@ 拘束圧力の下での圧縮強度 ( f b , f b , 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeGabaaUfmaabm aabaGaamOzamaaBaaaleaacaWGIbaabeaakiaacYcacaWGMbWaaSba aSqaaiaadkgaaeqaaOGaaiilaiaaicdaaiaawIcacaGLPaaaaaa@3FDB@ f b =1.2 f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadkgaaeqaaOGaaeypaiaabgdacaqGUaGaaeOmaiaadAga daWgaaWcbaGaam4yaaqabaaaaa@3E49@ r= 2/3 f 2 − s 0 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaiabg2 da9maakaaabaGaaGOmaiaac+cacaaIZaaaleqaaOWaaSaaaeaacaWG MbWaaSbaaSqaaiaaikdaaeqaaOGaeyOeI0Iaam4CamaaBaaaleaaca aIWaaabeaaaOqaaiaadAgadaWgaaWcbaGaam4yaaqabaaaaaaa@4105@ σ m = f 2 +2 s 0 3 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad2gaaeqaaOGaeyypa0ZaaSaaaeaacaWGMbWaaSbaaSqa aiaaikdaaeqaaOGaey4kaSIaaGOmaiaadohadaWgaaWcbaGaaGimaa qabaaakeaacaaIZaGaamOzamaaBaaaleaacaWGJbaabeaaaaaaaa@4216@ cos θ = − 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4yaiaac+ gacaGGZbGaeqiUdeNaeyypa0JaeyOeI0IaaGymaaaa@3D2D@ 図 13 と図 14は、破壊サーフェスを決定するポイントを示しています。 図 13. 平坦な応力面を有する破壊サーフェスのトレース 図 14. 静水圧軸に垂直な複数の断面を有する破壊トレース これらのプロットから、破壊エンベロープが凸型サーフェスではないことがわかります。 図 15 はこの挙動を示しています。 図 15. 2軸圧縮強度値の影響: 作用点以外の、特性に影響するすべての破壊点を固定した状態 図 16. 圧縮強度値の影響: 作用点以外の、特性に影響するすべての破壊点を固定した状態 図 17. 引張強度値の影響: 作用点以外の、特性に影響するすべての破壊点を固定した状態 この特定のケースにおいては、圧縮強度は変化していますが、 f t f c , f b f c , f 2 f c , s 0 f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGaaeaaca WGMbWaaSbaaSqaaiaadshaaeqaaaGcbaGaamOzamaaBaaaleaacaWG JbaabeaaaaGccaGGSaGaaeiiamaaliaabaGaamOzamaaBaaaleaaca WGIbaabeaaaOqaaiaadAgadaWgaaWcbaGaam4yaaqabaaaaOGaaiil aiaabccadaWccaqaaiaadAgadaWgaaWcbaGaaGOmaaqabaaakeaaca WGMbWaaSbaaSqaaiaadogaaeqaaaaakiaabYcacaqGGaWaaSGaaeaa caWGZbWaaSbaaSqaaiaaicdaaeqaaaGcbaGaamOzamaaBaaaleaaca WGJbaabeaaaaaaaa@4A37@ といったその他すべての比率は固定されています。これにより、図 18のようなエンベロープスケーリングが生じます。 図 18. 圧縮強度値の影響. 他のすべての比率は固定。 ここでは、LAW24と同じ強度を使用していますが、拘束圧縮強度 f 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaaikdaaeqaaaaa@393B@ には異なる値を使用しています。 図 19. 3軸破壊点 ( σ 1 , σ 2 , σ 3 ) = ( f 2 , s 0 , s 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbvg9s8 qqaqFr0xc9ps0xbba9s8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaamaabmaabaGaeq4Wdm3aaSbaaSqaaiaaigdaaeqaaOGaaiilaiab eo8aZnaaBaaaleaacaaIYaaabeaakiaacYcacqaHdpWCdaWgaaWcba GaaG4maaqabaaakiaawIcacaGLPaaacqGH9aqpdaqadaqaaiaadAga daWgaaWcbaGaaGOmaaqabaGccaGGSaGaam4CamaaBaaaleaacaaIWa aabeaakiaacYcacaWGZbWaaSbaaSqaaiaaicdaaeqaaaGccaGLOaGa ayzkaaaaaa@4DF9@ の影響を受ける平坦な応力面上の破壊エンベロープ f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGMbWaaS baaSqaaiaadogaaeqaaaaa@385D@ 、およびコンクリート破壊の定義に使用する r − σ m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey OeI0Iaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaaaa@3B23@ 空間での比率 f t f c , and f b f c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWccaqaai aadAgadaWgaaWcbaGaamiDaaqabaaakeaacaWGMbWaaSbaaSqaaiaa dogaaeqaaaaakiaacYcacaqGGaGaaeyyaiaab6gacaqGKbGaaeiiam aaliaabaGaamOzamaaBaaaleaacaWGIbaabeaaaOqaaiaadAgadaWg aaWcbaGaam4yaaqabaaaaaaa@435E@ は次のようになります: 図 20. 破壊曲線を決定するための各種試験(単軸引張、単軸圧縮、および2軸圧縮) ここで、破壊曲線は、 r = 2 J 2 = 2 3 σ V M MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbGaey ypa0ZaaOaaaeaacaaIYaGaamOsamaaBaaaleaacaaIYaaabeaaaeqa aOGaeyypa0ZaaOaaaeaadaWcaaqaaiaaikdaaeaacaaIZaaaaaWcbe aakiabeo8aZnaaBaaaleaacaWGwbGaamytaaqabaaaaa@4138@ を使用して定義され、 σ m = I 1 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyBaaqabaGccqGH9aqpdaWcaaqaaiaadMeadaWgaaWc baGaaGymaaqabaaakeaacaaIZaaaaaaa@3CDB@ は平均応力(圧力)、 I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaaigdaaeqaaaaa@3813@ および J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGjbWaaS baaSqaaiaaigdaaeqaaaaa@3813@ は第1および第2応力不変量です。 破壊曲線 r f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGYbWaaS baaSqaaiaadAgaaeqaaaaa@386C@ に達すると、材料は破壊します。 コンクリートの補強Radiossでは、2つの方法でコンクリートの補強をシミュレートできます。 1つは、ビームまたはトラス要素を複数の運動条件でコンクリートに結合する方法です。 もう1つは、LAW24のパラメータを直交異方性ソリッドプロパティ/PROP/TYPE6とともに使用し、補強方向を定義する方法です。LAW24のパラメータ α 1 , α 2 , α 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaaGymaaqabaGccaGGSaGaaeiiaiabeg7aHnaaBaaaleaa caaIYaaabeaakiaacYcacaqGGaGaeqySde2aaSbaaSqaaiaaiodaae qaaaaa@40AD@ を使用して、方向1、2、3について、全体のコンクリート断面積に対する補強断面積の比率を定義します。(9) α i = A r e a s t e e l A r e a c o n c r e t e MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyda WgaaWcbaGaamyAaaqabaGccqGH9aqpdaWcaaqaaiaadgeacaWGYbGa amyzaiaadggadaWgaaWcbaGaam4CaiaadshacaWGLbGaamyzaiaadY gaaeqaaaGcbaGaamyqaiaadkhacaWGLbGaamyyamaaBaaaleaacaWG JbGaam4Baiaad6gacaWGJbGaamOCaiaadwgacaWG0bGaamyzaaqaba aaaaaa@4DE4@ ここで、 σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyEaaqabaaaaa@394B@ は、補強の降伏応力です。補強としてスチールが使用される場合は、 σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHdpWCda WgaaWcbaGaamyEaaqabaaaaa@394B@ がスチールの降伏応力で、 E t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGfbWaaS baaSqaaiaadshaaeqaaaaa@384D@ が塑性相におけるスチールの弾性率です。 図 21. 補強(スチール)の応力-ひずみ曲線
コンクリート材料(/MAT/LAW81) LAW81は岩石またはコンクリート材料のモデル化に使用できます。 Drücker-Prager降伏基準 LAW81ではDrücker-Prager降伏基準を使用します。ここでは、降伏曲面と破壊曲面が同じです。降伏基準は以下のとおりです:(10) F = q ︸ J 2 part − r c ( p ) ⋅ ( p tan ϕ + c ) ︸ I 1 part = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbGaey ypa0ZaaGbaaeaacaWGXbaaleaacaWGkbWaaSbaaWqaaiaaikdaaeqa aSGaaeiiaiaabchacaqGHbGaaeOCaiaabshaaOGaayjo+dGaeyOeI0 YaaGbaaeaaciGGYbWaaSbaaSqaaiaacogaaeqaaOWaaeWaaeaacaWG WbaacaGLOaGaayzkaaGaeyyXIC9aaeWaaeaacaWGWbGaciiDaiaacg gacaGGUbGaeqy1dyMaey4kaSIaam4yaaGaayjkaiaawMcaaaWcbaGa amysamaaBaaameaacaaIXaaabeaaliaabccacaqGWbGaaeyyaiaabk hacaqG0baakiaawIJ=aiabg2da9iaaicdaaaa@5BE0@ ここで、 q MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ 以下の条件におけるvon Mises応力: q = σ V M = 3 J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0Jaeq4Wdm3aaSbaaSqaaiaadAfacaWGnbaabeaakiabg2da9maa kaaabaGaaG4maiaadQeadaWgaaWcbaGaaGOmaaqabaaabeaaaaa@3F8A@ p MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ 圧力は以下のように定義されます: p = 1 3 I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey ypa0ZaaSaaaeaacaaIXaaabaGaaG4maaaacaWGjbWaaSbaaSqaaiaa igdaaeqaaaaa@3B96@ 図 22. 降伏曲面(LAW81) 降伏曲面は2つの部分で表されます: 線形部分( p ≤ p a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey izImQaamiCamaaBaaaleaacaWGHbaabeaaaaa@3B0F@ )、ここではスケール関数が r c ( p ) = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGYbWaaS baaSqaaiaacogaaeqaaOWaaeWaaeaacaWGWbaacaGLOaGaayzkaaGa eyypa0JaaGymaaaa@3CB2@ で、von Mises応力が圧力に線形比例します:(11) q = p tan ϕ + c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0JaamiCaiGacshacaGGHbGaaiOBaiabew9aMjabgUcaRiaadoga aaa@3FB2@ ここで、 c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ 粘度。せん断強度による降伏エンベロープを制限します。 c = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGJbGaey ypa0JaaGimaaaa@3906@ の場合、材料に引張強度はありません。 ϕ 内部摩擦の角度。降伏エンベロープの勾配を定義します。 c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbaaaa@3754@ および ϕ は、Mohr-Coulomb降伏曲面の定義にも使用されます。Drücker-Prage降伏曲面は、Mohr-Coulomb降伏曲面を滑らかにしたものです。 降伏曲面の2つ目の部分( p a < p < p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadggaaeqaaOGaeyipaWJaamiCaiabgYda8iaadchadaWg aaWcbaGaamOyaaqabaaaaa@3D74@ )は、cap制限をシミュレートします。岩石またはコンクリート材料での圧力の増加により、材料の降伏が増加しますが、圧力が十分に大きくなると、岩石またはコンクリート材料は圧壊されます。cap制限のあるDrücker-Pragerモデルを使用して、この挙動をモデル化できます。cap制限はの部分で定義され、以下のスケール関数を使用します:(12) r c ( p ) = 1 − ( p − p a p b − p a ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGYbWaaS baaSqaaiaacogaaeqaaOWaaeWaaeaacaWGWbaacaGLOaGaayzkaaGa eyypa0ZaaOaaaeaacaaIXaGaeyOeI0YaaeWaaeaadaWcaaqaaiaadc hacqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGcbaGaamiCamaa BaaaleaacaWGIbaabeaakiabgkHiTiaadchadaWgaaWcbaGaamyyaa qabaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaqabaaa aa@4934@ von Mises応力は以下のようになります:(13) q = 1 − ( p − p a p b − p a ) 2 ⋅ ( p tan ϕ + c ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0ZaaOaaaeaacaaIXaGaeyOeI0YaaeWaaeaadaWcaaqaaiaadcha cqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGcbaGaamiCamaaBa aaleaacaWGIbaabeaakiabgkHiTiaadchadaWgaaWcbaGaamyyaaqa baaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaqabaGccq GHflY1daqadaqaaiaadchaciGG0bGaaiyyaiaac6gacqaHvpGzcqGH RaWkcaWGJbaacaGLOaGaayzkaaaaaa@50CC@ ここで、 p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadkgaaeqaaaaa@3866@ 曲線はfct_IDPb入力を使用して定義されます。 p a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadkgaaeqaaaaa@3866@ 入力 α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHXoqyaa a@37FD@ 率の値を使用してRadiossによって計算されます。 p a = α ⋅ p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadggaaeqaaOGaeyypa0JaeqySdeMaeyyXICTaamiCamaa BaaaleaacaWGIbaabeaaaaa@3F66@ ここで、 0 < α < 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaaIWaGaey ipaWJaeqySdeMaeyipaWJaaGymaaaa@3B7A@ 。 ここで、 p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ は、降伏曲線の最大ポイントです。ここで、 ∂ F ∂ p ( p 0 ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kaadAeaaeaacqGHciITcaWGWbaaamaabmaabaGaamiCamaa BaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiabg2da9iaaicdaaa a@4028@ p = p b MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey ypa0JaamiCamaaBaaaleaacaWGIbaabeaaaaa@3A61@ の場合、 r c ( p b ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGYbWaaS baaSqaaiaacogaaeqaaOWaaeWaaeaacaWGWbWaaSbaaSqaaiaadkga aeqaaaGccaGLOaGaayzkaaGaeyypa0JaaGimaaaa@3DCE@ となり、降伏関数は、 q = 0 ⋅ ( p tan ϕ + c ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGXbGaey ypa0JaaGimaiabgwSixpaabmaabaGaamiCaiGacshacaGGHbGaaiOB aiabew9aMjabgUcaRiaadogaaiaawIcacaGLPaaacqGH9aqpcaaIWa aaaa@45FF@ となります。これは材料が圧壊されることを意味します。 入力パラメータ ϕ , c , p b , α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHvpGzca GGSaGaaeiiaiaadogacaGGSaGaaeiiaiaadchadaWgaaWcbaGaamOy aaqabaGccaGGSaGaaeiiaiabeg7aHbaa@40B8@ を、Drücker–Prager降伏曲面用に特定する必要があります。これらのパラメータをフィッティングさせるには、少なくとも4つの試験が必要です。最も簡単なケースでは、単軸引張と単軸圧縮を使用して、線形部分 ϕ , and c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHvpGzca GGSaGaaeiiaiaabggacaqGUbGaaeizaiaabccacaWGJbaaaa@3DC0@ を特定できます。 p b , and α MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadkgaaeqaaOGaaiilaiaabccacaqGHbGaaeOBaiaabsga caqGGaGaeqySdegaaa@3EC1@ を特定するには、2軸圧縮試験と圧縮 / 圧縮試験が必要です(RD-E: 4701 Kupfer試験でのコンクリートの検証のCC00およびCC01 )。 図 23. さまざまな荷重条件を示すLAW81の降伏曲面 金属など、ほとんどの材料では、塑性ひずみの増分は降伏曲面に垂直と見なすことができます。ただし、降伏曲面に垂直な塑性ひずみの増分が岩石やコンクリートの材料に使用された場合、塑性体積膨張が過大に見積もられます。したがって、非関連塑性流れ則がこれらの材料で使用されます。LAW81では、塑性流れ関数 G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ は次のように定義されます: G = q − p ⋅ tan ψ = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamyCaiabgkHiTiaadchacqGHflY1ciGG0bGaaiyyaiaac6ga cqaHipqEcqGH9aqpcaaIWaaaaa@43B1@ 、右記の場合; p ≤ p a MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey izImQaamiCamaaBaaaleaacaWGHbaabeaaaaa@3B0F@ G = q − tan ψ ( p − ( p − p a ) 2 2 ( p 0 − p a ) ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamyCaiabgkHiTiGacshacaGGHbGaaiOBaiabeI8a5naabmaa baGaamiCaiabgkHiTmaalaaabaWaaeWaaeaacaWGWbGaeyOeI0Iaam iCamaaBaaaleaacaWGHbaabeaaaOGaayjkaiaawMcaamaaCaaaleqa baGaaGOmaaaaaOqaaiaaikdadaqadaqaaiaadchadaWgaaWcbaGaaG imaaqabaGccqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGccaGL OaGaayzkaaaaaaGaayjkaiaawMcaaiabg2da9iaaicdaaaa@5184@ 、右記の場合; p a < p ≤ p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaadggaaeqaaOGaeyipaWJaamiCaiabgsMiJkaadchadaWg aaWcbaGaaGimaaqabaaaaa@3DF8@ G = F MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamOraaaa@38FB@ 、右記の場合; p > p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbGaey Opa4JaamiCamaaBaaaleaacaaIWaaabeaaaaa@3A36@ 圧力は p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ であるため、降伏関数 F MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ と塑性流れ関数 G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ は同じであり、次の条件が満たされます:(14) G ( p 0 ) = F ( p 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaai ikaiaadchadaWgaaWcbaGaaGimaaqabaGccaGGPaGaeyypa0JaamOr aiaacIcacaWGWbWaaSbaaSqaaiaaicdaaeqaaOGaaiykaaaa@3F77@ (15) ∂G ∂p | p 0 = ∂F ∂p | p 0 =0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kaadEeaaeaacqGHciITcaWGWbaaamaaeeaabaWaaSbaaSqa aiaadchadaWgaaadbaGaaGimaaqabaaaleqaaaGccaGLhWoacqGH9a qpdaWcaaqaaiabgkGi2kaadAeaaeaacqGHciITcaWGWbaaamaaeeaa baWaaSbaaSqaaiaadchadaWgaaadbaGaaGimaaqabaaaleqaaaGcca GLhWoacqGH9aqpcaaIWaaaaa@49BF@ 圧力 p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ は、 ∂ F ∂ p | p 0 = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai abgkGi2kaadAeaaeaacqGHciITcaWGWbaaamaaeeaabaWaaSbaaSqa aiaadchadaWgaaadbaGaaGimaaqabaaaleqaaaGccaGLhWoacqGH9a qpcaaIWaaaaa@406B@ である降伏曲面を使用して計算できます。ここで G MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbaaaa@372A@ は次のように定義されます:(16) G = q − tan ψ ( p − ( p − p a ) 2 2 ( p 0 − p a ) ) = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbGaey ypa0JaamyCaiabgkHiTiGacshacaGGHbGaaiOBaiabeI8a5naabmaa baGaamiCaiabgkHiTmaalaaabaWaaeWaaeaacaWGWbGaeyOeI0Iaam iCamaaBaaaleaacaWGHbaabeaaaOGaayjkaiaawMcaamaaCaaaleqa baGaaGOmaaaaaOqaaiaaikdadaqadaqaaiaadchadaWgaaWcbaGaaG imaaqabaGccqGHsislcaWGWbWaaSbaaSqaaiaadggaaeqaaaGccaGL OaGaayzkaaaaaaGaayjkaiaawMcaaiabg2da9iaaicdaaaa@5184@ パラメータ ψ は、関数内の圧力 p 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGWbWaaS baaSqaaiaaicdaaeqaaaaa@3839@ でvon Mises応力を使用することで特定できます。 図 24. 塑性流れによるLAW81の降伏曲面