/MAT/LAW14 (COMPSO)

ブロックフォーマットキーワード この材料則は、主に1方向の複合材をモデル化するために設計されたTsai-Wu定式化を使用して、直交異方性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。

方向3の非線形は方向2の非線形と同じになり、複合マトリックス材料の挙動を表します。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。/MAT/LAW12 (3D_COMP)はこの材料の強化版で、LAW14の代わりに使用する必要があります。

フォーマット

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW14/mat_ID/unit_IDまたは/MAT/COMPSO/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 ref 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    
α Ef c ε ˙ 0 ICC  

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

(実数)

 
n グローバル塑性硬化の指数

デフォルト = 1.0(実数)

 
fmax Tsai-Wu基準の制限の最大値 3

デフォルト = 1010(実数)

 
W p ref 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

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 12 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 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3792@ 繊維体積率 5

デフォルト = 0.0(実数)

 
Ef 繊維ヤング率

デフォルト = 0.0(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 s ]
ICC ひずみ速度効果フラグ 3
= 1(デフォルト)
fに対するひずみ速度効果ありmax
= 2
fに対するひずみ速度効果なしmax

(整数)

 

例(金属)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  kg                  cm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/COMPSO/1/1
Metal
#              RHO_I
               .0078                   
#                E11                 E22                 E33
                  10                 100                   1
#               NU12                NU23                NU31
                   0                   0                   0
#                G12                 G23                 G31
                   0                   0                   0
#           SIGMA_T1            SIGMA_T2            SIGMA_T3               DELTA
                1E31                1E31                1E31                   0
#                  B                   n                fmax               Wpref
                1E31                1E31                1E31                   0
#          sigma_1yt           sigma_2yt           sigma_1yc           sigma_2yc
                1E31                1E31                1E31                1E31
#         sigma_12yt          sigma_12yc          sigma_23yt          sigma_23yc
                1E31                1E31                1E31                1E31
#              ALPHA                 E_f                   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指定されます。
  2. 弾性相での応力-ひずみ関係。
    応力とひずみは次のように結合されます:(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 21 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

    γ 12 = 1 2 G 12 σ 12 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS baaSqaaiaaigdacaaIYaaabeaakiabg2da9maalaaabaGaaGymaaqa aiaaikdacaWGhbWaaSbaaSqaaiaaigdacaaIYaaabeaaaaGccqaHdp WCdaWgaaWcbaGaaGymaiaaikdaaeqaaaaa@41B7@ ν 21 E 22 = ν 12 E 11 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aH9oGBdaWgaaWcbaGaaGOmaiaaigdaaeqaaaGcbaGaamyramaaBaaa leaacaaIYaGaaGOmaaqabaaaaOGaeyypa0ZaaSaaaeaacqaH9oGBda WgaaWcbaGaaGymaiaaikdaaeqaaaGcbaGaamyramaaBaaaleaacaaI XaGaaGymaaqabaaaaaaa@42CB@

    γ 23 = 1 2 G 23 σ 23 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS baaSqaaiaaikdacaaIZaaabeaakiabg2da9maalaaabaGaaGymaaqa aiaaikdacaWGhbWaaSbaaSqaaiaaikdacaaIZaaabeaaaaGccqaHdp WCdaWgaaWcbaGaaGOmaiaaiodaaeqaaaaa@41BD@ ν 32 E 33 = ν 23 E 22 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaamaalaaabaGaeqyVd42aaSbaaSqaaiaaiodacaaIYaaabeaaaOqa aiaadweadaWgaaWcbaGaaG4maiaaiodaaeqaaaaakiabg2da9maala aabaGaeqyVd42aaSbaaSqaaiaaikdacaaIZaaabeaaaOqaaiaadwea daWgaaWcbaGaaGOmaiaaikdaaeqaaaaaaaa@461B@

    γ 31 = 1 2 G 31 σ 31 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS baaSqaaiaaiodacaaIXaaabeaakiabg2da9maalaaabaGaaGymaaqa aiaaikdacaWGhbWaaSbaaSqaaiaaiodacaaIXaaabeaaaaGccqaHdp WCdaWgaaWcbaGaaG4maiaaigdaaeqaaaaa@41BA@ ν 13 E 11 = ν 31 E 33 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aH9oGBdaWgaaWcbaGaaGymaiaaiodaaeqaaaGcbaGaamyramaaBaaa leaacaaIXaGaaGymaaqabaaaaOGaeyypa0ZaaSaaaeaacqaH9oGBda WgaaWcbaGaaG4maiaaigdaaeqaaaGcbaGaamyramaaBaaaleaacaaI ZaGaaG4maaqabaaaaaaa@42CF@

    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、
    • 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: (4)
      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@
    複合マトリックス材料を表すために、方向2と3の非線形挙動は同じであると見なされます。複合マトリックス材料の降伏応力(方向2と3)は、次のように関係すると見なされます:
    σ 3 y c = σ 2 y c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbc9v8 qqaqFr0xb9pg0xb9qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs 0dXdHuk9fr=xfr=xfrpeWZqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiabeo8aZnaaDaaaleaacaaIZaGaamyEaaqaaiaadogaaaGccqGH 9aqpcqaHdpWCdaqhaaWcbaGaaGOmaiaadMhaaeaacaWGJbaaaaaa@447D@ σ 3 y t = σ 2 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbc9v8 qqaqFr0xb9pg0xb9qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs 0dXdHuk9fr=xfr=xfrpeWZqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiabeo8aZnaaDaaaleaacaaIZaGaamyEaaqaaiaadshaaaGccqGH 9aqpcqaHdpWCdaqhaaWcbaGaaGOmaiaadMhaaeaacaWG0baaaaaa@449F@
    σ 31 y c = σ 12 y c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbc9v8 qqaqFr0xb9pg0xb9qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs 0dXdHuk9fr=xfr=xfrpeWZqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiabeo8aZnaaDaaaleaacaaIZaGaaGymaiaadMhaaeaacaWGJbaa aOGaeyypa0Jaeq4Wdm3aa0baaSqaaiaaigdacaaIYaGaamyEaaqaai aadogaaaaaaa@45F3@ σ 31 y t = σ 12 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbc9v8 qqaqFr0xb9pg0xb9qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs 0dXdHuk9fr=xfr=xfrpeWZqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiabeo8aZnaaDaaaleaacaaIZaGaaGymaiaadMhaaeaacaWGJbaa aOGaeyypa0Jaeq4Wdm3aa0baaSqaaiaaigdacaaIYaGaamyEaaqaai aadogaaaaaaa@45F3@
    • 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:(5)
      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 r e f 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 r e d u c e d = ( 1 D i ) σ t i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaDa aaleaacaWGPbaabaGaamOCaiaadwgacaWGKbGaamyDaiaadogacaWG LbGaamizaaaakiabg2da9iaacIcacaaIXaGaeyOeI0IaamiramaaBa aaleaacaWGPbaabeaakiaacMcacqaHdpWCdaWgaaWcbaGaamiDaiaa dMgaaeqaaaaa@491D@ としてスケーリングされます。 D i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadseadaWgaa WcbaGaamyAaaqabaaaaa@37CF@ の値は時間ステップ D i = i δ i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGebWaaS baaSqaaiaadMgaaeqaaOGaeyypa0ZaaabuaeaacqaH0oazdaWgaaWc baGaamyAaaqabaaabaGaamyAaaqab0GaeyyeIuoaaaa@3F17@ ごとに更新されます。 D i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadseadaWgaa WcbaGaamyAaaqabaaaaa@37CF@ 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 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadseadaWgaa WcbaGaamyAaaqabaaaaa@37CF@ 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 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey yXICTaamyramaaBaaaleaacaWGMbaabeaakiabgwSixlabew7aLnaa BaaaleaacaaIXaGaaGymaaqabaaaaa@415E@ と同じように追加されます。