/MAT/LAW102 (DPRAG2)

ブロックフォーマットキーワード この材料則は、拡張Drücker-Prager降伏基準に基づくもので、岩石-コンクリートのように内部摩擦を伴う材料のモデル化に使用されます。これらの材料の塑性挙動は、材料内の圧力に依存します。

この材料則は/MAT/LAW10 (DRAGP1)に似ています; 唯一の違いは、降伏基準がMohr-Coulombパラメータ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGJbaaaa@39BF@ および ϕ から計算される点です。狙いは、Mohr-Coulomb基準に適合するDrücker-Prager基準を計算することにあります。

フォーマット

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW102/mat_ID/unit_IDまたは/MAT/DPRAG2/mat_ID/unit_ID
mat_title
ρ i                
Iform                  
E ν MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyVd4gaaa@37AE@            
c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGJbaaaa@39BF@ ϕ Amax        
Pmin                

定義

フィールド 内容 SI単位の例
mat_ID 材料識別子

(整数、最大10桁)

 
unit_ID 単位識別子

(整数、最大10桁)

 
mat_title 材料のタイトル

(文字、最大100文字)

 
ρ i 初期密度

(実数)

[ kg m 3 ]
Iform 定式化フラグ 1
= 1(デフォルト)
外接基準
= 2
中央基準
= 3
内接基準

(整数)

 
E ヤング率

(実数)

[ Pa ]
ν MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyVd4gaaa@37AE@ ポアソン比

(実数)

 
c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGJbaaaa@39BF@ 粘着(Mohr-Coulombパラメータ)

(実数)

[ Pa ]
ϕ 内部摩擦角(Mohr-Coulombパラメータ)

(実数)

[ deg ]
Amax 降伏基準限度

デフォルト = 1030(実数)

[ Pa 2 ]
Pmin 最小圧力(通常、負またはゼロ、引張の場合は正)

デフォルト = -1030(実数)

[ Pa ]

例(コンクリート)

#RADIOSS STARTER
/UNIT/1
unit for mat
                   g                  mm                 ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/DPRAG2/102/1
Concrete
#              RHO_I
               .0024
#    Iform
         2
#                  E                  NU
               61000                 .17 
#                  c                 PHI                AMAX
                  50                  40                 0.0
#              P_min       
                   0            
/EOS/POLYNOMIAL/102/1
Concrete
#                 C0                  C1                  C2                  C3
                   0               10000                   0                   0
#                 C4                  C5                 Psh                Rho0
                   0                   0                   0               .0024
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

コメント

  1. 拡張Drücker-Prager降伏基準は次のように定義されます:


    図 1.

    この材料則の狙いは、A0A1A2パラメータをMohr-Coulombパラメータ c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGJbaaaa@39BF@ (粘着)および ϕ (内部摩擦の角度)から自動的に計算することにあります。

    Mohr-Coulomb基準は通常次のように定義されます:
    τ = c σ n tan ϕ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdqNaey ypa0Jaam4yaiabgkHiTiabeo8aZnaaBaaaleaacaWGUbaabeaakiGa cshacaGGHbGaaiOBaiabew9aMbaa@421C@
    ここで、
    τ
    せん断応力
    σ n MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaad6gaaeqaaaaa@38D9@
    法線応力
    c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGJbaaaa@39BF@
    粘着
    ϕ
    内部摩擦の角度
    Mohr-Coulombパラメータから、3つの異なる拡張Drücker-Prager降伏基準を計算することができます。


    図 2. Mohr-CoulombパラメータからのDrücker-Prager降伏基準

    以下の値が計算されます: A 0 = k 2 ,   A 1 = 6 k α ,   A 2 = 9 α 2   MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIWaaabeaakiabg2da9iaadUgadaahaaWcbeqaaiaaikda aaGccaGGSaGaaeiiaiaadgeadaWgaaWcbaGaaGymaaqabaGccqGH9a qpcaaI2aGaam4Aaiabeg7aHjaacYcacaqGGaGaamyqamaaBaaaleaa caaIYaaabeaakiabg2da9iaaiMdacqaHXoqydaahaaWcbeqaaiaaik daaaGccaqGGaaaaa@49FE@

    ここで、
    基準 k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36E6@ α
    外接 k = 6. c . cos ( φ ) 3 . ( 3 sin ( φ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabbaGcbaGaam4Aaiabg2 da9maalaaabaGaaGOnaiaac6cacaWGJbGaaiOlaiGacogacaGGVbGa ai4CaiaacIcacqaHgpGAcaGGPaaabaWaaOaaaeaacaaIZaWaaSbaaS qaaaqabaaabeaakiaac6cacaGGOaGaaG4maiabgkHiTiGacohacaGG PbGaaiOBaiaacIcacqaHgpGAcaGGPaGaaiykaaaaaaa@4B99@ α = 2. s i n ( φ ) 3 . ( 3 sin ( φ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabbaGcbaGaeqySdeMaey ypa0ZaaSaaaeaacaaIYaGaaiOlaiaacohacaGGPbGaaiOBaiaacIca cqaHgpGAcaGGPaaabaWaaOaaaeaacaaIZaWaaSbaaSqaaaqabaaabe aakiaac6cacaGGOaGaaG4maiabgkHiTiGacohacaGGPbGaaiOBaiaa cIcacqaHgpGAcaGGPaGaaiykaaaaaaa@4AAD@
    中央 k = 6. c . cos ( φ ) 3 . ( 3 + sin ( φ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabbaGcbaGaam4Aaiabg2 da9maalaaabaGaaGOnaiaac6cacaWGJbGaaiOlaiGacogacaGGVbGa ai4CaiaacIcacqaHgpGAcaGGPaaabaWaaOaaaeaacaaIZaWaaSbaaS qaaaqabaaabeaakiaac6cacaGGOaGaaG4maiabgUcaRiGacohacaGG PbGaaiOBaiaacIcacqaHgpGAcaGGPaGaaiykaaaaaaa@4B8E@ α = 2. s i n ( φ ) 3 . ( 3 + sin ( φ ) ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabbaGcbaGaeqySdeMaey ypa0ZaaSaaaeaacaaIYaGaaiOlaiaacohacaGGPbGaaiOBaiaacIca cqaHgpGAcaGGPaaabaWaaOaaaeaacaaIZaWaaSbaaSqaaaqabaaabe aakiaac6cacaGGOaGaaG4maiabgUcaRiGacohacaGGPbGaaiOBaiaa cIcacqaHgpGAcaGGPaGaaiykaaaaaaa@4AA2@
    内接 k = 3. c . cos ( φ ) 9 + 3 sin 2 ( φ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabbaGcbaGaam4Aaiabg2 da9maalaaabaGaaG4maiaac6cacaWGJbGaaiOlaiGacogacaGGVbGa ai4CaiaacIcacqaHgpGAcaGGPaaabaWaaOaaaeaacaaI5aGaey4kaS IaaG4maiGacohacaGGPbGaaiOBamaaCaaaleqabaGaaGOmaaaakiaa cIcacqaHgpGAcaGGPaaaleqaaaaaaaa@4A4D@ α = sin ( φ ) 9 + 3 sin 2 ( φ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabbaGcbaGaeqySdeMaey ypa0ZaaSaaaeaaciGGZbGaaiyAaiaac6gacaGGOaGaeqOXdOMaaiyk aaqaamaakaaabaGaaGyoaiabgUcaRiaaiodaciGGZbGaaiyAaiaac6 gadaahaaWcbeqaaiaaikdaaaGccaGGOaGaeqOXdOMaaiykaaWcbeaa aaaaaa@47F8@
  2. 圧力 P ( μ , E ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGqbWaaeWaaeaacqaH8oqBcaGGSaGaamyraaGaayjkaiaawMca aaaa@3E65@ は状態方程式(/EOS)を介して定義されます。
    ここで、
    P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGqbaaaa@39AC@
    材料内の圧力
    μ
    μ = ρ ρ 0 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiVd0Maey ypa0ZaaSaaaeaacqaHbpGCaeaacqaHbpGCdaWgaaWcbaGaaGimaaqa baaaaOGaeyOeI0IaaGymaaaa@3EDA@ で与えられる体積ひずみ
    E = E int V MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraiabg2 da9maalaaabaGaamyramaaBaaaleaaciGGPbGaaiOBaiaacshaaeqa aaGcbaGaamOvaaaaaaa@3C8A@
    エネルギー密度

    除荷:

    μ μ max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiVd0Maey izImQaeqiVd02aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaa@3E17@ の場合、除荷体積弾性率 B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=He9 q8qqQ8frFve9Fve9Ff0dmeaacaGacmGadaWaaiqacaabaiaafaaake aacaWGcbaaaa@399E@ は除荷 / 再載荷パスに使用されます。それぞれの μ μ max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiVd02aaS baaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaa@3AAC@ を上回るもの)で、除荷経路は荷重経路と同じです。

  3. Drücker-Prager降伏基準は次のように与えられます:(1)
    F = J 2 ( A 0 + A 1 P + A 2 P 2 )

    mat_law10B
    図 3.
    ここで、
    J 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsamaaBa aaleaacaaIYaaabeaaaaa@37AE@
    偏差応力の第2不変量で、 σ V M = 3 J 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadAfacaWGnbaabeaakiabg2da9maakaaabaGaaG4maiaa dQeadaWgaaWcbaGaaGOmaaqabaaabeaaaaa@3D27@
    P
    圧力で、 P = I 1 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiabg2 da9maalaaabaGaeyOeI0IaamysamaaBaaaleaacaaIXaaabeaaaOqa aiaaiodaaaaaaa@3B4B@ で与えられる圧力( I 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaaIXaaabeaaaaa@37AC@ は第1応力不変量)
    A 1 = A 2 = 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqamaaBa aaleaacaaIXaaabeaakiabg2da9iaadgeadaWgaaWcbaGaaGOmaaqa baGccqGH9aqpcaaIWaaaaa@3C2C@
    降伏基準はフォンミーゼス( σ V M = 3 A 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadAfacaWGnbaabeaakiabg2da9maakaaabaGaaG4maiaa dgeadaWgaaWcbaGaaGimaaqabaaabeaaaaa@3D1C@

    多項式には少なくとも1つのルートが必要で、増大する必要があります。

  4. 圧力は常に、全圧力です。相対圧力をモデル化するには、/EOSPshパラメータを用いて圧力出力をシフトする必要があります。
  5. 降伏の最大Amaxは、降伏関数が下記になった際のものです。(2)
    J 2 =min( A max ,( A 0 + A 1 P+ A 2 P 2 ) ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsamaaBa aaleaacaaIYaaabeaakiabg2da9iGac2gacaGGPbGaaiOBamaabmaa baGaamyqamaaBaaaleaaciGGTbGaaiyyaiaacIhaaeqaaOGaaiilai aacIcacaWGbbWaaSbaaSqaaiaaicdaaeqaaOGaey4kaSIaamyqamaa BaaaleaacaaIXaaabeaakiaadcfacqGHRaWkcaWGbbWaaSbaaSqaai aaikdaaeqaaOGaamiuamaaCaaaleqabaGaaGOmaaaakiaacMcaaiaa wIcacaGLPaaaaaa@4C77@