/MAT/LAW14 (COMPSO)

Block Format Keyword This law describes an orthotropic solid material using the Tsai-Wu formulation that is mainly designed to model uni-directional composites. This material is assumed to be 3D orthotropic-elastic before the Tsai-Wu criterion is reached. The material becomes nonlinear afterwards.

The nonlinearity in direction 3 is the same as that in direction 2 to represent the behavior of a composite matrix material. The Tsai-Wu criterion can be set dependent on the plastic work and strain rate in each of the orthotropic directions and in shear to model material hardening. Stress based orthotropic criterion for brittle damage and failure is available. /MAT/LAW12 (3D_COMP) is an improved version of this material and should be used instead of LAW14.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW14/mat_ID/unit_ID or /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

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID Unit Identifier.

(Integer, maximum 10 digits)

mat_title Material title.

(Character, maximum 100 characters)

ρ i Initial density.

(Real)

[ kg m 3 ]
E11 Young's modulus in direction 1.

(Real)

[ Pa ]
E22 Young's modulus in direction 2.

(Real)

[ Pa ]
E33 Young's modulus in direction 3.

(Real)

[ Pa ]
ν 12 Poisson's ratio between directions 1 and 2.

(Real)

ν 23 Poisson's ratio between directions 2 and 3.

(Real)

ν 31 Poisson's ratio between directions 3 and 1.

(Real)

G12 Shear modulus in direction 12.

(Real)

[ Pa ]
G23 Shear modulus in direction 23.

(Real)

[ Pa ]
G31 Shear modulus in direction 31.

(Real)

[ Pa ]
σ t 1 Stress at the beginning of composite tensile/compressive failure in direction 1. 4

Default = 1030 (Real)

[ Pa ]
σ t 2 Stress at the beginning of composite tensile/compressive failure in direction 2. 4

Default = σ t 1 (Real)

[ Pa ]
σ t 3 Stress at the beginning of composite tensile/compressive failure in direction 3. 4

Default = σ t 2 (Real)

[ Pa ]
δ Maximum damage factor. 4

Default = 0.05 (Real)

B Global plastic hardening parameter.

(Real)

n Global plastic hardening exponent.

Default = 1.0 (Real)

fmax Maximum value of the Tsai-Wu criterion limit. 3

Default = 1010 (Real)

W p ref MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba WccaqGxbaddaqhaaqaaiaadchaaeaacaWGYbGaamyzaiaadAgaaaaa aa@3E4A@ Reference plastic work per unit solid volume.

Default = 1.0 (in local unit system) (Real)

[ J m 3 ]
σ 1 y t Yield stress in tension in direction 1.

Default = 0.0 (Real)

[ Pa ]
σ 2 y t Yield stress in tension in direction 2.

Default = 0.0 (Real)

[ Pa ]
σ 1 y c Yield stress in compression in direction 1.

Default = 0.0 (Real)

[ Pa ]
σ 2 y c Yield stress in compression in direction 2.

Default = 0.0 (Real)

[ Pa ]
σ 12 y t Yield stress in tensile shear in direction 12.

Default = 0.0 (Real)

[ Pa ]
σ 12 y c Yield stress in compressive shear in direction 12.

Default = 0.0 (Real)

[ Pa ]
σ 23 y t Yield stress in tensile shear in direction 23.

Default = 0.0 (Real)

[ Pa ]
σ 23 y c Yield stress in compressive shear in direction 23.

Default = 0.0 (Real)

[ Pa ]
α MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3792@ Fiber volume fraction. 5

Default = 0.0 (Real)

Ef Fiber Young's modulus.

Default = 0.0 (Real)

[ Pa ]
c Global strain rate coefficient.
= 0
No strain rate effect

(Real)

ε ˙ 0 Reference strain rate.

(Real)

[ 1 s ]
ICC Strain rate effect flag. 3
= 1 (Default)
Strain rate effect on fmax
= 2
No strain rate effect on fmax

(Integer)

Example (Metal)

#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----|

Comments

  1. This material requires an orthotropic solid property (/PROP/TYPE6 (SOL_ORTH), /PROP/TYPE21 (TSH_ORTH) or /PROP/TYPE22 (TSH_COMP)). It can only be used with solid elements for a 3-dimensional analysis. This law is compatible with 10-node tetrahedron and 4-node tetrahedron elements. The orthotropic material directions are specified in the property entries.
  2. Stress-strain relation in elastic phase.

    The stresses and strains are connected as:

    ε 11 = 1 E 11 σ 11 ν 21 E 22 σ 22 ν 31 E 33 σ 33
    ε 22 = 1 E 22 σ 22 ν 21 E 11 σ 11 ν 32 E 33 σ 33
    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@

    Where,
    ε i j
    Strains
    σ i j
    Stresses
    γ 12 , γ 23 and γ 31
    Distortions in the corresponding material directions
    For example, for γ 12 :
    Figure 1.

    mat_law12_distortion
  3. Tsai-Wu criterion
    The material is assumed to be elastic until the Tsai-Wu criterion is fulfilled. After exceed the Tsai-Wu criterion limit F( W p * , ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacaWGxbWaa0baaSqaaiaadchaaeaacaGGQaaaaOGaaiilaiqbew7a LzaacaGaaiykaaaa@3D33@ , the material becomes nonlinear.
    • If F(σ)<F( W p * , ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacqaHdpWCcaGGPaGaeyipaWJaciOraiGacIcacaWGxbWaa0baaSqa aiaadchaaeaacaGGQaaaaOGaaiilaiqbew7aLzaacaGaaiykaaaa@4221@ : elastic
    • If F(σ)>F( W p * , ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacqaHdpWCcaGGPaGaeyOpa4JaciOraiGacIcacaWGxbWaa0baaSqa aiaadchaaeaacaGGQaaaaOGaaiilaiqbew7aLzaacaGaaiykaaaa@4225@ : nonlinear
    Where,
    • Stress F ( σ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGgbWaae WaaeaacqaHdpWCaiaawIcacaGLPaaaaaa@3A76@ in element for Tsai-Wu criterion computed as:
      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@
    The coefficients of the Tsai-Wu criterion are determined from the limiting stresses when the material becomes nonlinear in directions 1, 2, 3 or 12, 23, 31 (shear) in compression or tension as:
    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@
    The nonlinear behavior in directions 2 and 3 is assumed to be the same to represent the composite matrix material. It is assumed that yield stresses of the composite matrix material (in directions 2 and 3) are related as:
    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@ is the variable Tsai-Wu criterion limit defined:
      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@
      Where,
      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@
      Reference plastic work
      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@
      Relative plastic work
      B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGcbaaaa@3725@
      Plastic hardening parameter
      n MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGcbaaaa@3725@
      Plastic hardening exponent
      ε ˙ 0
      Reference true strain rate
      c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGcbaaaa@3725@
      Strain rate coefficient
      F ( W p * , ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiGacAeadaqadaqaaiaadEfadaqhaaWcbaGaamiCaaqaaiaacQca aaGccaGGSaGafqyTduMbaiaaaiaawIcacaGLPaaaaaa@40AA@ the maximum value of the Tsai-Wu criterion limit depends on ICC:
      If ICC=1
      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@
      If ICC=2
      f max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadAgadaWgaaWcbaGaciyBaiaacggacaGG4baabeaaaaa@3D2A@

      Where, 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. Stress damage

    When the limiting stress value of σ t i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiabeo8aZnaaBa aaleaacaWG0bGaamyAaaqabaaaaa@39C2@ is reached in tension, then the corresponding stress value is scaled as 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@ . The value of D i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadseadaWgaa WcbaGaamyAaaqabaaaaa@37CF@ is updated on each time step D i = i δ i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGebWaaS baaSqaaiaadMgaaeqaaOGaeyypa0ZaaabuaeaacqaH0oazdaWgaaWc baGaamyAaaqabaaabaGaamyAaaqab0GaeyyeIuoaaaa@3F17@ . After D i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadseadaWgaa WcbaGaamyAaaqabaaaaa@37CF@ reaches the value of 1 the stress in corresponding direction is set to 0. The damage is irreversible, if a value of D i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadseadaWgaa WcbaGaamyAaaqabaaaaa@37CF@ is attained the material will not reach any lower damage value.

  5. Fiber reinforcement

    These parameters allow the user to define additional fiber reinforcement in the 11 direction. Additional stress in direction 11 will be added equal to α E f ε 11 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdeMaey yXICTaamyramaaBaaaleaacaWGMbaabeaakiabgwSixlabew7aLnaa BaaaleaacaaIXaGaaGymaaqabaaaaa@415E@ .