/MAT/LAW12 (3D_COMP)

ブロックフォーマットキーワード この材料則は、通常は複合材のモデル化に使用するTsai-Wu定式化を使用してソリッド材料を記述します。この材料は、Tsai-Wu基準を満たすまでは、3D直交異方性弾性であると見なされます。

材料は、その後、非線形となります。Tsai-Wu基準は、材料硬化をモデル化するよう、せん断における各直交異方性方向での塑性仕事およびひずみ速度に応じて設定できます。脆性損傷および破壊のための応力ベースの直交異方性基準を使用できます。この材料は/MAT/LAW14 (COMPSO)を一般化および改善したものです。

フォーマット

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW12/mat_ID/unit_IDまたは/MAT/3D_COMP/mat_ID/unit_ID
mat_title
ρ i                
E11 E22 E33        
ν 12 ν 23 ν 31        
G12 G23 G31        
σ t 1 σ t 2 σ t 3 δ    
B n fmax W p r e f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba WccaqGxbaddaqhaaqaaiaadchaaeaacaWGYbGaamyzaiaadAgaaaaa aa@3E4A@    
σ 1 y t σ 2 y t σ 1 y c σ 2 y c    
σ 12 y t σ 12 y c σ 23 y t σ 23 y c    
σ 3 y t σ 3 y c σ 13 y t σ 13 y c    
α Ef c ε ˙ 0    

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 ]
E11 方向1のヤング率

(実数)

[ Pa ]
E22 方向2のヤング率

(実数)

[ Pa ]
E33 方向3のヤング率

(実数)

[ Pa ]
ν 12 方向1と2の間のポアソン比

(実数)

 
ν 23 方向2と3の間のポアソン比

(実数)

 
ν 31 方向3と1の間のポアソン比

(実数)

 
G12 方向12におけるせん断係数

(実数)

[ Pa ]
G23 方向23におけるせん断係数

(実数)

[ Pa ]
G31 方向31におけるせん断係数

(実数)

[ Pa ]
σ t 1 方向1における複合引張 / 圧縮破壊の開始時点の応力 4

デフォルト = 1030(実数)

[ Pa ]
σ t 2 方向2における複合引張 / 圧縮破壊の開始時点の応力 4

デフォルト = σ t 1 (実数)

[ Pa ]
σ t 3 方向3における複合引張 / 圧縮破壊の開始時点の応力 4

デフォルト = σ t 2 (実数)

[ Pa ]
δ 最大損傷係数 4

デフォルト = 0.05(実数)

 
B グローバル塑性硬化パラメータ 3

(実数)

 
n グローバル塑性硬化の指数

デフォルト = 1.0(実数)

 
f max Tsai-Wu基準の制限の最大値 3

デフォルト = 1010(実数)

 
W p r e f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba WccaqGxbaddaqhaaqaaiaadchaaeaacaWGYbGaamyzaiaadAgaaaaa aa@3E4A@ 単位ソリッド体積あたりの基準塑性仕事

デフォルト = 1.0(局所単位系)(実数)

[ J m 3 ]
σ 1 y t 方向1の引張りにおける降伏応力 3

デフォルト = 0.0(実数)

[ Pa ]
σ 2 y t 方向2の引張りにおける降伏応力

デフォルト = 0.0(実数)

[ Pa ]
σ 1 y c 方向1の圧縮における降伏応力

デフォルト = 0.0(実数)

[ Pa ]
σ 2 y c 方向2の圧縮における降伏応力

デフォルト = 0.0(実数)

[ Pa ]
σ 12 y t 方向12の引張せん断における降伏応力

デフォルト = 0.0(実数)

[ Pa ]
σ 2 y c 方向12の圧縮せん断における降伏応力

デフォルト = 0.0(実数)

[ Pa ]
σ 23 y t 方向23の引張せん断における降伏応力

デフォルト = 0.0(実数)

[ Pa ]
σ 23 y c 方向23の圧縮せん断における降伏応力

デフォルト = 0.0(実数)

[ Pa ]
α 繊維体積率 5

(実数)

 
Ef 繊維ヤング率 5

(実数)

[ Pa ]
c グローバルひずみ速度係数
= 0
ひずみ速度効果はなし

(実数)

 
ε ˙ 0 参照ひずみ速度

(実数)

[ 1 2 ]
ICC ひずみ速度効果フラグ 3
=1(デフォルト)
ひずみ速度効果あり f max
= 2
ひずみ速度効果なし f max

(整数)

 

例(Carbon)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW12/1/1
carbon
#              RHO_I
              1.5E-9
#                E11                 E22                 E33
               64000               60000                5000
#               NU12                NU23                NU31
                 .07                 .07                 .07
#                G12                 G23                 G31
                4000                2000                2000
#           sigma_t1            sigma_t2            sigma_t3               delta
                   0                   0                   0                   0
#                  B                   n                fmax               Wpref
                  50                  .5                   0                   0
#          sigma_1yt           sigma_2yt           sigma_1yc           sigma_2yc
                 600                 500                 600                 600
#         sigma_12yt          sigma_12yc          sigma_23yt          sigma_23yc
                 100                 100                  30                  30
#          sigma_3yt           sigma_3yc          sigma_13yt          sigma_13yc
                  50                  50                 100                 100
#              alpha                  Ef                   c          EPS_RATE_0       ICC
                   0                   0                   0                   0         0
#---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. この材料には、直交異方性ソリッドプロパティ(/PROP/TYPE6 (SOL_ORTH)/PROP/TYPE21 (TSH_ORTH)または/PROP/TYPE22 (TSH_COMP))が必要です。これは、3次元解析用のソリッド要素でのみ使用できます。この材料則は、10節点四面体および4節点四面体の要素と適合性があります。直交異方性材料の方向は、プロパティエントリで設定されます。
  2. 弾性相での応力-ひずみの関係。
    応力とひずみは次のように関係付けられます:(1)
    ε 11 = 1 E 11 σ 11 ν 21 E 22 σ 22 ν 31 E 33 σ 33
    (2)
    ε 22 = 1 E 22 σ 22 ν 12 E 11 σ 11 ν 32 E 33 σ 33
    (3)
    ε 33 = 1 E 33 σ 33 ν 13 E 11 σ 11 ν 23 E 22 σ 22
    (4)
    γ 12 = 1 2 G 12 σ 12 ν 21 E 22 = ν 12 E 11 γ 23 = 1 2 G 23 σ 23 ν 32 E 33 = ν 23 E 22 γ 31 = 1 2 G 31 σ 31 ν 13 E 11 = ν 31 E 33
    ここで、
    ε i j
    ひずみ
    σ i j
    応力
    γ 12 γ 23 および γ 31
    対応する材料方向の歪み
    例えば、 γ 12 の場合:

    mat_law12_distortion
    図 1.
  3. Tsai-Wu基準:
    この材料は、Tsai-Wu基準を満たすまでは、弾性であると見なされます。Tsai-Wu基準の制限 F ( W p * , ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacaWGxbWaa0baaSqaaiaadchaaeaacaGGQaaaaOGaaiilaiqbew7a LzaacaGaaiykaaaa@3D33@ を超えると、材料は次のように非線形になります:
    • F ( σ ) < F ( W p * , ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacqaHdpWCcaGGPaGaeyipaWJaciOraiGacIcacaWGxbWaa0baaSqa aiaadchaaeaacaGGQaaaaOGaaiilaiqbew7aLzaacaGaaiykaaaa@4221@ の場合: 弾性
    • F ( σ ) > F ( W p * , ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacqaHdpWCcaGGPaGaeyOpa4JaciOraiGacIcacaWGxbWaa0baaSqa aiaadchaaeaacaGGQaaaaOGaaiilaiqbew7aLzaacaGaaiykaaaa@4225@ の場合: 非線形
    ここで、
    • ここで、Tsai-Wu基準における要素内の応力 F ( σ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGgbWaae WaaeaacqaHdpWCaiaawIcacaGLPaaaaaa@3A76@ は次のように計算されます: (5)
      F ( σ ) = F 1 σ 1 + F 2 σ 2 + F 3 σ 3 + F 11 σ 1 2 + F 22 σ 2 2 + F 33 σ 3 2 + F 44 σ 12 2 + F 55 σ 23 2 + F 66 σ 31 2 + 2 F 12 σ 1 σ 2 + 2 F 23 σ 2 σ 3 + 2 F 13 σ 1 σ 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakqaabeqaaiGacA eadaqadaqaaiabeo8aZbGaayjkaiaawMcaaiabg2da9iaadAeadaWg aaWcbaGaaGymaaqabaGccqaHdpWCdaWgaaWcbaGaaGymaaqabaGccq GHRaWkcaWGgbWaaSbaaSqaaiaaikdaaeqaaOGaeq4Wdm3aaSbaaSqa aiaaikdaaeqaaOGaey4kaSIaamOramaaBaaaleaacaaIZaaabeaaki abeo8aZnaaBaaaleaacaaIZaaabeaaaOqaauaabeqabeaaaeaaaaqb aeqabeqaaaqaaaaafaqabeqabaaabaaaauaabeqabeaaaeaaaaGaey 4kaSIaamOramaaBaaaleaacaaIXaGaaGymaaqabaGccqaHdpWCdaqh aaWcbaGaaGymaaqaaiaaikdaaaGccqGHRaWkcaWGgbWaaSbaaSqaai aaikdacaaIYaaabeaakiabeo8aZnaaDaaaleaacaaIYaaabaGaaGOm aaaakiabgUcaRiaadAeadaWgaaWcbaGaaG4maiaaiodaaeqaaOGaeq 4Wdm3aa0baaSqaaiaaiodaaeaacaaIYaaaaOGaey4kaSIaamOramaa BaaaleaacaaI0aGaaGinaaqabaGccqaHdpWCdaqhaaWcbaGaaGymai aaikdaaeaacaaIYaaaaOGaey4kaSIaamOramaaBaaaleaacaaI1aGa aGynaaqabaGccqaHdpWCdaqhaaWcbaGaaGOmaiaaiodaaeaacaaIYa aaaOGaey4kaSIaamOramaaBaaaleaacaaI2aGaaGOnaaqabaGccqaH dpWCdaqhaaWcbaGaaG4maiaaigdaaeaacaaIYaaaaaGcbaqbaeqabe qaaaqaaaaafaqabeqabaaabaaaauaabeqabeaaaeaaaaqbaeqabeqa aaqaaaaacqGHRaWkcaaIYaGaamOramaaBaaaleaacaaIXaGaaGOmaa qabaGccqaHdpWCdaWgaaWcbaGaaGymaaqabaGccqaHdpWCdaWgaaWc baGaaGOmaaqabaGccqGHRaWkcaaIYaGaamOramaaBaaaleaacaaIYa GaaG4maaqabaGccqaHdpWCdaWgaaWcbaGaaGOmaaqabaGccqaHdpWC daWgaaWcbaGaaG4maaqabaGccqGHRaWkcaaIYaGaamOramaaBaaale aacaaIXaGaaG4maaqabaGccqaHdpWCdaWgaaWcbaGaaGymaaqabaGc cqaHdpWCdaWgaaWcbaGaaG4maaqabaaaaaa@9283@
    Tsai-Wu基準の係数は、材料が圧縮または引張りの方向1、2、3または12、23、31(せん断)で非線形になった場合の制限応力から、次のように決定されます:
    F 1 = 1 σ 1 y c + 1 σ 1 y t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaaabeaakiabg2da9iabgkHiTmaalaaabaGaaGymaaqa aiabeo8aZnaaDaaaleaacaaIXaGaamyEaaqaaiaadogaaaaaaOGaey 4kaSYaaSaaaeaacaaIXaaabaGaeq4Wdm3aa0baaSqaaiaaigdacaWG 5baabaGaamiDaaaaaaaaaa@455B@ F 2 = 1 σ 2 y c + 1 σ 2 y t MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIYaaabeaakiabg2da9iabgkHiTmaalaaabaGaaGymaaqa aiabeo8aZnaaDaaaleaacaaIYaGaamyEaaqaaiaadogaaaaaaOGaey 4kaSYaaSaaaeaacaaIXaaabaGaeq4Wdm3aa0baaSqaaiaaikdacaWG 5baabaGaamiDaaaaaaaaaa@455E@ F 3 = 1 σ 3 y c + 1 σ 3 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAeadaWgaaWcbaGaaG4maaqabaGccqGH9aqpcqGHsisldaWc aaqaaiaaigdaaeaacqaHdpWCdaqhaaWcbaGaaG4maiaadMhaaeaaca WGJbaaaaaakiabgUcaRmaalaaabaGaaGymaaqaaiabeo8aZnaaDaaa leaacaaIZaGaamyEaaqaaiaadshaaaaaaaaa@48A9@
    F 11 = 1 σ 1 y c σ 1 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGymaaqabaGccqGH9aqpdaWcaaqaaiaaigdaaeaa cqaHdpWCdaqhaaWcbaGaaGymaiaadMhaaeaacaWGJbaaaOGaeq4Wdm 3aa0baaSqaaiaaigdacaWG5baabaGaamiDaaaaaaaaaa@437B@ F 22 = 1 σ 2 y c σ 2 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIYaGaaGOmaaqabaGccqGH9aqpdaWcaaqaaiaaigdaaeaa cqaHdpWCdaqhaaWcbaGaaGOmaiaadMhaaeaacaWGJbaaaOGaeq4Wdm 3aa0baaSqaaiaaikdacaWG5baabaGaamiDaaaaaaaaaa@437F@ F 33 = 1 σ 3 y c σ 3 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAeadaWgaaWcbaGaaG4maiaaiodaaeqaaOGaeyypa0ZaaSaa aeaacaaIXaaabaGaeq4Wdm3aa0baaSqaaiaaiodacaWG5baabaGaam 4yaaaakiabeo8aZnaaDaaaleaacaaIZaGaamyEaaqaaiaadshaaaaa aaaa@46CC@
    F 44 = 1 σ 12 y c σ 12 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaaS baaSqaaiaaisdacaaI0aaabeaakiabg2da9maalaaabaGaaGymaaqa aiabeo8aZnaaDaaaleaacaaIXaGaaGOmaiaadMhaaeaacaWGJbaaaO Gaeq4Wdm3aa0baaSqaaiaaigdacaaIYaGaamyEaaqaaiaadshaaaaa aaaa@4561@ F 55 = 1 σ 23 y c σ 23 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGgbWaaS baaSqaaiaaiwdacaaI1aaabeaakiabg2da9maalaaabaGaaGymaaqa aiabeo8aZnaaDaaaleaacaaIYaGaaG4maiaadMhaaeaacaWGJbaaaO Gaeq4Wdm3aa0baaSqaaiaaikdacaaIZaGaamyEaaqaaiaadshaaaaa aaaa@4567@ F 66 = 1 σ 31 y c σ 31 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAeadaWgaaWcbaGaaGOnaiaaiAdaaeqaaOGaeyypa0ZaaSaa aeaacaaIXaaabaGaeq4Wdm3aa0baaSqaaiaaiodacaaIXaGaamyEaa qaaiaadogaaaGccqaHdpWCdaqhaaWcbaGaaG4maiaaigdacaWG5baa baGaamiDaaaaaaaaaa@4848@
    F 12 = 1 2 ( F 11 F 22 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGOmaaqabaGccqGH9aqpcqGHsisldaWcaaqaaiaa igdaaeaacaaIYaaaamaakaaabaWaaeWaaeaacaWGgbWaaSbaaSqaai aaigdacaaIXaaabeaakiaadAeadaWgaaWcbaGaaGOmaiaaikdaaeqa aaGccaGLOaGaayzkaaaaleqaaaaa@427D@ F 23 = 1 2 ( F 22 F 33 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAeadaWgaaWcbaGaaGOmaiaaiodaaeqaaOGaeyypa0JaeyOe I0YaaSaaaeaacaaIXaaabaGaaGOmaaaadaGcaaqaamaabmaabaGaam OramaaBaaaleaacaaIYaGaaGOmaaqabaGccaWGgbWaaSbaaSqaaiaa iodacaaIZaaabeaaaOGaayjkaiaawMcaaaWcbeaaaaa@45CB@ F 13 = 1 2 ( F 11 F 33 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAeadaWgaaWcbaGaaGymaiaaiodaaeqaaOGaeyypa0JaeyOe I0YaaSaaaeaacaaIXaaabaGaaGOmaaaadaGcaaqaamaabmaabaGaam OramaaBaaaleaacaaIXaGaaGymaaqabaGccaWGgbWaaSbaaSqaaiaa iodacaaIZaaabeaaaOGaayjkaiaawMcaaaWcbeaaaaa@45C8@
    • F ( W p * , ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiGacAeadaqadaqaaiaadEfadaqhaaWcbaGaamiCaaqaaiaacQca aaGccaGGSaGafqyTduMbaiaaaiaawIcacaGLPaaaaaa@40AA@ は、次のように定義された可変のTsai-Wu基準の制限:(6)
      F ( W p * , ε ˙ ) = [ 1 + B ( W p * ) n ] [ 1 + c ln ( ε ˙ ε ˙ 0 ) ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiGacAeadaqadaqaaiaadEfadaqhaaWcbaGaamiCaaqaaiaacQca aaGccaGGSaGafqyTduMbaiaaaiaawIcacaGLPaaacqGH9aqpdaWada qaaiaaigdacqGHRaWkcaWGcbWaaeWaaeaacaWGxbWaa0baaSqaaiaa dchaaeaacaGGQaaaaaGccaGLOaGaayzkaaWaaWbaaSqabeaacaWGUb aaaaGccaGLBbGaayzxaaGaeyyXIC9aamWaaeaacaaIXaGaey4kaSIa am4yaiabgwSixlGacYgacaGGUbWaaeWaaeaadaWcaaqaaiqbew7aLz aacaaabaGafqyTduMbaiaadaWgaaWcbaGaaGimaaqabaaaaaGccaGL OaGaayzkaaaacaGLBbGaayzxaaaaaa@5C47@
      ここで、
      W p ref MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaBaaaleaacaWGWbaabeaakmaaCaaaleqabaGaamOCaiaa dwgacaWGMbaaaaaa@3DAC@
      参照塑性仕事
      W p * = W p W p r e f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadEfadaqhaaWcbaGaamiCaaqaaiaacQcaaaGccqGH9aqpdaWc aaqaaiaadEfadaWgaaWcbaGaamiCaaqabaaakeaacaWGxbWaa0baaS qaaiaadchaaeaacaWGYbGaamyzaiaadAgaaaaaaaaa@43DC@
      相対塑性仕事
      B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGcbaaaa@3725@
      塑性硬化パラメータ
      n MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGcbaaaa@3725@
      塑性硬化指数
      ε ˙ 0
      参照真ひずみ速度
      c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGcbaaaa@3725@
      ひずみ速度係数
      F ( W p * , ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiGacAeadaqadaqaaiaadEfadaqhaaWcbaGaamiCaaqaaiaacQca aaGccaGGSaGafqyTduMbaiaaaiaawIcacaGLPaaaaaa@40AA@ ICCに応じたTsai-Wu基準の制限の最大値:
      ICC=1の場合
      f max ( 1 + c ln ( ε ˙ ε ˙ o ) ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAgadaWgaaWcbaGaciyBaiaacggacaGG4baabeaakiabgwSi xpaabmaabaGaaGymaiabgUcaRiaadogacqGHflY1ciGGSbGaaiOBam aabmaabaWaaSaaaeaacuaH1oqzgaGaaaqaaiqbew7aLzaacaWaaSba aSqaaiaad+gaaeqaaaaaaOGaayjkaiaawMcaaaGaayjkaiaawMcaaa aa@4DDD@
      ICC=2の場合
      f max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAgadaWgaaWcbaGaciyBaiaacggacaGG4baabeaaaaa@3D2A@

      ここで、 f max = ( σ max σ y ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaaciGGTbGaaiyyaiaacIhaaeqaaOGaeyypa0ZaaeWaaeaadaWc aaqaaiabeo8aZnaaBaaaleaaciGGTbGaaiyyaiaacIhaaeqaaaGcba Gaeq4Wdm3aaSbaaSqaaiaadMhaaeqaaaaaaOGaayjkaiaawMcaamaa CaaaleqabaGaaGOmaaaaaaa@4537@

  4. 応力損傷:
    引張で σ t i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa aaleaacaWG0bGaamyAaaqabaaaaa@39C2@ の制限応力値に達した場合、対応する応力値は σ i reduced = ( 1 D i ) σ t i としてスケーリングされます。損傷の値 D i は各時間ステップで増分損傷パラメータ δ と共に更新されます。 (7)
    D i = i δ i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGebWaaS baaSqaaiaadMgaaeqaaOGaeyypa0ZaaabuaeaacqaH0oazdaWgaaWc baGaamyAaaqabaaabaGaamyAaaqab0GaeyyeIuoaaaa@3F17@

    D i の値が1に達すると、対応する方向の応力が0に設定されます。損傷は逆転できないので、 D i の値が到達した場合、材料がそれ以上低い損傷値に達することはありません。

  5. 繊維補強:

    これらのパラメータにより、方向11の繊維補強を追加で定義できます。追加の方向11の応力は、 α E f ε 11 と同じように追加されます。