CRASURV Formulation (Iform= 1)

Block Format Keyword This law describes the composite shell and solid material using the CRASURV formulation.

This material is assumed to be orthotropic-elastic before the Tsai-Wu criterion is reached. The material becomes nonlinear afterwards. For solid elements, the material is assumed to be linearly elastic in the transverse direction. 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. Strain and plastic energy criterion for brittle damage and failure is available. A simplified delamination criterion based on out-of-plane shear angle can be used.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW25/mat_ID/unit_ID or /MAT/COMPSH/mat_ID/unit_ID
mat_title
ρi                
E11 E22 ν12 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyVd42aaSbaaSqaaiaaigdacaaIYaaabeaaaaa@3CD1@ Iform   E33
G12 G23 G31 εf1 εf2
εt1 εm1 εt2 εm2 dmax
Composite Plasticity Hardening
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Wpmax   Ioff WP_fail ratio    
Global Composite Plasticity Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
c ε˙0 α       ICCglobal
Composite Plasticity in Tension Directions 1 and 2
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
σ1yt b1t n1t σ1maxt c1t
ε1t1 ε1t2 σ1rst W1pmaxt    
σ2yt b2t n2t σ2maxt c2t
ε2t1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aa0baaSqaaiaaikdaaeaacaWG0bGaaGymaaaaaaa@3DBA@ ε2t2 σ2rst W2pmaxt MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaWcdaqfGaqabeqabaGaamiDaaqaaiaabEfadaqhaaqaaWGaaeOmaSGaamiCaaqaaiGac2gacaGGHbGaaiiEaaaaaaaaaa@4049@    
Composite Plasticity in Compression Directions 1 and 2
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
σ1yc b1c n1c σ1maxc c1c
ε1c1 ε1c2 σ1rsc MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4Wdm3aa0baaSqaaiaabgdacaWGYbGaam4Caaqaaiaadogaaaaaaa@3EF1@ W1pmaxc    
σ2yc b2c n2c σ2maxc c2c
ε2c1 ε2c2 σ2rsc MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4Wdm3aa0baaSqaaiaabkdacaWGYbGaam4Caaqaaiaadogaaaaaaa@3EF2@ W2pmaxc    
Composite Plasticity in Shear
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
σ12y b12 n12 σ12max c12
ε121 ε122 σ12rs W12pmax    
Delamination
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
γini γmax d3max        
Strain Rate Filtering
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Fsmooth Fcut              

Definitions

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)

 
ρi Initial density.

(Real)

[kgm3]
E11 Young's modulus in direction 1.

(Real)

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

(Real)

[Pa]
ν12 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyVd42aaSbaaSqaaiaaigdacaaIYaaabeaaaaa@3CD1@ Poisson's ratio .

(Real)

 
Iform Formulation flag. 1
= 1
CRASURV formulation.

(Integer)

 
E33 Young's modulus in direction 33. 2

(Real)

[Pa]
G12 Shear modulus in direction 12.

(Real)

[Pa]
G23 Shear modulus in direction 23.

(Real)

[Pa]
G31 Shear modulus in direction 31.

(Real)

[Pa]
εf1 Maximum tensile strain for element deletion in material direction 1.

Default = 1.2 x 1020 (Real)

εf2 Maximum tensile strain for element deletion in material direction 2.

Default = 1.2 x 1020 (Real)

εt1 Tensile failure strain in the material direction 1 at which stress starts to reduce. 4

Default = 1.0 x 1020 (Real)

εm1 Maximum tensile strain in material direction 1 at which the stress in the element is set to a value dependent on dmax. 4

Default = 1.1 x 1020 (Real)

εt2 Tensile failure strain in the material direction 2 at which stress starts to reduce.

Default = 1.0 x 1020 (Real)

εm2 Maximum tensile strain in material direction 2 at which the stress in the element is set to a value dependent on dmax.

Default = 1.1 x 1020 (Real)

dmax Maximum damage factor (dmax < 1). 4

Default = 0.999 (Real)

Wpmax Global maximum plastic work per unit shell volume.

Default = 1020 (Real)

[Jm3]
Ioff Flag that controls shell and thick shell element deletion depending on failure modes in the element layers. 4
= 0
Shell is deleted if maximum plastic work for one element layer.
= 1
Shell is deleted if maximum plastic work for all element layers.
= 2
Shell is deleted if for each element layer, Condition1:{eithermax.plasticworkreachedorε1>εm1indirection1ord1>dmaxindirection1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=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@9CCE@
= 3
Shell is deleted if for each element layer, Condition2:{eithermax.plasticworkreachedorε2>εm2indirection2ord2>dmaxindirection2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=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@9E60@
= 4
Shell is deleted if for each element layer, condition 1 and condition 2 are satisfied.
= 5
Shell is deleted if all element layers, condition 1 or condition 2 is satisfied.
= 6
Shell is deleted if for each element layer condition 1 or condition 2 is satisfied.

(Integer)

WP_fail Directional maximum plastic work failure formulation. 5
=0 (Default)
Directional maximum plastic work Wijpmax MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGxbWaa0baaSqaaiaadMgacaWGQbGaamiCaaqaaiGac2gacaGGHbGaaiiEaaaaaaa@3E17@ defines rupture only if residual stress greater than yield stress. Otherwise, global maximum plastic work Wpmax MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaWccaWGxbaddaqhaaqaaiaadchaaeaaciGGTbGaaiyyaiaacIhaaaaaaa@3E54@ defines rupture.
=1
Directional maximum plastic work Wijpmax MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGxbWaa0baaSqaaiaadMgacaWGQbGaamiCaaqaaiGac2gacaGGHbGaaiiEaaaaaaa@3E17@ defines rupture.
 
Ratio Ratio parameter which controls the deletion of shell elements based on the number of failed layers. 4
< 0.0
The element will be deleted if, all but one layer fails (that is, the number of layers that did not fail is equation to 1).
> 0.0
The element will be deleted if numberoffailedlayersnumberoftotallayersratio .

Default = 1.0 (Real)

 
c Global strain rate coefficient for plastic work criteria.
= 0.0
No strain rate dependency.

(Real)

ε˙0 Reference strain rate.

(Real)

[1s]
α Reduction factor for F12 coefficient calculation in Tsai-Wu criterion.

Default set to 1.0 (Real)

ICCglobal Global strain rate effect flag. 4
= 1 (Default)
Srain rate effect on σ1maxt , σ2maxt , σ1maxc , σ2maxc , σ12max is taken into account, but there is no strain rate effect on Wpmax
= 2
No strain rate effect on σ1maxt , σ2maxt , σ1maxc , σ2maxc , σ12max and Wpmax .
= 3
Strain rate effect on σ1maxt , σ2maxt , σ1maxc , σ2maxc , σ12max is taken into account, but there is no strain rate effect on Wpmax .
= 4
Strain rate effect on Wpmax is taken into account, but there is no strain rate effect on σ1maxt , σ2maxt , σ1maxc , σ2maxc , σ12max .

(Integer)

σ1yt Yield stress in tension in direction 1.

Default = 0.0 (Real)

[Pa]
b1t Plastic hardening parameter in tension in direction 1.

Default = 0.0 (Real)

n1t Plastic hardening exponent in tension in direction 1.

Default = 1.0 (Real)

σ1maxt Maximum stress in tension in direction 1.

Default = 1020 (Real)

[Pa]
c1t Strain rate coefficient in tension in direction 1.
= 0
No strain rate dependency.

Default = c (Real)

ε1t1 Initial softening strain in tension in the material direction 1.

Default = 1.0 x 1020 (Real)

ε1t2 Maximum softening strain in tension in the material direction 1.

Default = 1.2ε1t1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaaigdaaeaacaWG0bGaaGymaaaaaaa@3FE2@ (Real)

σ1rst Residual stress in tension in direction 1.

Default = 103σ1yt MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWCdaqhaaWcbaGaaGymaiaadMhaaeaacaWG0baaaaaa@416E@ (Real)

[Pa]
W1pmaxt MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaWcdaqfGaqabeqabaGaamiDaaqaaiaabEfadaqhaaqaaWGaaeymaSGaamiCaaqaaiGac2gacaGGHbGaaiiEaaaaaaaaaa@4048@ Directional maximum plastic work per unit shell volume in tension in direction 1. 4

Default = 1020 (Real)

[Jm3]
σ2yt Yield stress in tension in direction 2.

Default = 0.0 (Real)

[Pa]
b2t Plastic hardening parameter in tension in direction 2.

Default = 0.0 (Real)

n2t Plastic hardening exponent in tension in direction 2.

Default = 1.0 (Real)

σ2maxt Maximum stress in tension in direction 2.

Default = 1020 (Real)

[Pa]
c2t Strain rate coefficient in tension in direction 2.
= 0
No strain rate dependency

Default = c (Real)

ε2t1 Initial softening strain in tension in the material direction 2.

Default = 1.0 x 1020 (Real)

ε2t2 Maximum softening strain in tension in direction 2.

Default = 1.2ε1t2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaaigdaaeaacaWG0bGaaGOmaaaaaaa@3FE3@ (Real)

σ2rst Residual stress in tension in direction 2.

Default = 103σ2yt MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWCdaqhaaWcbaGaaGOmaiaadMhaaeaacaWG0baaaaaa@416F@ (Real)

[Pa]
W2pmaxt Directional maximum plastic work per unit shell volume in tension in direction 2. 4

Default = 1020 (Real)

[Jm3]
σ1yc Yield stress in compression in direction 1.

Default = 0.0 (Real)

[Pa]
b1c Plastic hardening parameter in compression in direction 1.

Default = b2t (Real)

n1c Plastic hardening exponent in compression in direction 1.

Default = n2t (Real)

σ1maxc Maximum stress in compression in direction 1.

Default = 1020 (Real)

[Pa]
c1c Strain rate coefficient in compression in direction 1.
= 0
No strain rate dependency.

Default = c (Real)

ε1c1 Initial softening strain in compression in the material direction 1.

Default = 1.0 x 1020 (Real)

ε1c2 Maximum softening strain in compression in the material direction 1.

Default = 1.2ε1c1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaaigdaaeaacaWGJbGaaGymaaaaaaa@3FD1@ (Real)

σ1rsc Residual stress in compression in direction 1.

Default = 103σ1yc MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWCdaqhaaWcbaGaaGymaiaadMhaaeaacaWGJbaaaaaa@415D@ (Real)

[Pa]
W1pmaxc Directional maximum plastic work per unit shell volume in compression in direction 1.

Default = 1020 (Real)

[Jm3]
σ2yc Yield stress in compression in direction 2.

Default = 0.0 (Real)

[Pa]
b2c Plastic hardening parameter in compression in direction 2.

Default = b2t (Real)

n2c Plastic hardening exponent in compression in direction 2.

Default = n2t (Real)

σ2maxc Maximum stress in compression in direction 2.

Default = 1020 (Real)

[Pa]
c2c Strain rate coefficient in compression in direction 2.
= 0
No strain rate dependency.

Default = c (Real)

ε2c1 Initial softening strain in compression in the material direction 2.

Default = 1.0 x 1020 (Real)

ε2c2 Maximum softening strain in compression in the material direction 2.

Default = 1.2ε2c1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaabkdaaeaacaWGJbGaaeymaaaaaaa@3FC4@ (Real)

σ2rsc Residual stress in compression in direction 2.

Default = 103σ2yc MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWCdaqhaaWcbaGaaGOmaiaadMhaaeaacaWGJbaaaaaa@415E@ (Real)

[Pa]
W2pmaxc Directional maximum plastic work per unit shell volume in compression in direction 2. 4

Default = 1020 (Real)

[Jm3]
σ12y Yield stress in direction 12 (in 45 degree of fiber direction).

Default = 0.0 (Real)

[Pa]
b12 Plastic hardening parameter in direction 12.

Default = b2t (Real)

n12 Plastic hardening exponent in direction 12.

Default = n2t (Real)

σ12max Maximum stress in direction 12.

Default = 1020 (Real)

[Pa]
ε121 Strain rate coefficient in direction 12.
= 0
No strain rate dependency.

Default = c (Real)

ε121 Initial softening strain in the material direction 12.

Default = 1.0 x 1020 (Real)

ε122 Maximum softening strain in the material direction 12.

Default = 1.2ε121 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaaigdacaqGYaaabaGaaGymaaaaaaa@3F9E@ (Real)

σ12rs Residual stress in direction 12.

Default = 103σ12y MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWCdaWgaaWcbaGaaGymaiaaikdacaWG5baabeaaaaa@4130@ (Real)

[Pa]
W12pmax Directional maximum plastic work per unit shell volume in direction 12. 4

Default = 1020 (Real)

[Jm3]
γini Out of plane shear strain when delamination begins. 4

Default = 1020 (Real)

γmax Out of plane shear strain when delamination ends, and the element is deleted. 4

Default = 1.1e20 (Real)

d3max Maximum delamination damage factor (d3max < 1). 4

Default = 1.0 (Real)

Fsmooth Strain rate smoothing flag.
= 0 (Default)
Strain rate smoothing is inactive.
= 1
Strain rate smoothing is active.

(Integer)

Fcut Cutoff frequency for strain rate smoothing.

Default = 1020 (Real)

[Hz]

Example (Carbon composite)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/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/COMPSH/1/1
carbone based tissu
#              RHO_I
               .0015                   0
#                E11                 E22                NU12     Iform                           E33
               56275               54868                .042         1                             0
#                G12                 G23                 G31              EPS_f1              EPS_f2
                4212                4212                4212                   0                   0
#             EPS_t1              EPS_m1              EPS_t2              EPS_m2               d_max
             .016305                 .02             .014131                .016                   0
#              Wpmax                          Ioff   WP_fail               ratio
                  15                             6         0                  .5
#                  c          EPS_rate_0               alpha                              ICC_global
                   0                   0                   0                                       0
#            sig_1yt                b_1t                n_1t           sig_1maxt                c_1t
              917.59                   0                   1                 919                   0
#            EPS_1t1             EPS_1t2          SIGMA_rst1            Wpmax_t1
                   0                   0                   0                   0
#            sig_2yt                b_2t                n_2t           sig_2maxt                c_2t
              775.38                   0                   1                 777                   0
#            EPS_2t1             EPS_2t2            sig_rst2            Wpmax_t2
                   0                   0                   0                   0
#            sig_1yc                b_1c                n_1c           sig_1maxc                c_1c
                 355                 .17                 .84              708.87                   0
#            EPS_1c1             EPS_1c2            sig_rsc1            Wpmax_c1
               .0226                .025                   0                   0
#            sig_2yc                b_2c                n_2c           sig_2maxc                c_2c
                 355                 .17                 .84              702.97                   0
#            EPS_2c1             EPS_2c2            sig_rsc2            Wpmax_c2
               .0226                .025                   0                   0
#            sig_12y                b_12                n_12           sig_12max                c_12
                  30      2.872290896763                  .3              132.57                   0
#           EPS_12t1            EPS_12t2           sig_rs_12            Wpmax_12
                   0                   0                   0                   0
#          GAMMA_ini           GAMMA_max              d3_max
                   0                   0                   0
#  Fsmooth                Fcut
         0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Example (Kevlar)

#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/COMPSH/1/1
KEVLAR
#              RHO_I
              1.4E-9
#                E11                 E22                NU12     Iform                           E33
               87000               87000                  .3         1                             0
#                G12                 G23                 G31              EPS_f1              EPS_f2
                2200                2200                2200                   0                   0
#             EPS_t1              EPS_m1              EPS_t2              EPS_m2               d_max
                .015                .017                .015                .017                   0
#              Wpmax                          Ioff   WP_fail               ratio
                   0                             6         0                  .5
#                  c          EPS_rate_0               alpha                              ICC_global
                   0                   0                   0                                       0
#            sig_1yt                b_1t                n_1t           sig_1maxt                c_1t
                 650                   0                   1                   0                   0
#            EPS_1t1             EPS_2t1          SIGMA_rst1            Wpmax_t1
                   0                   0                   0                   0
#            sig_2yt                b_2t                n_2t           sig_2maxt                c_2t
                 650                   0                   1                   0                   0
#            EPS_1t2             EPS_2t2            sig_rst2            Wpmax_t2
                   0                   0                   0                   0
#            sig_1yc                b_1c                n_1c           sig_1maxc                c_1c
                 335                   0                   1                 650                   0
#            EPS_1c1             EPS_2c1            sig_rsc1            Wpmax_c1
                 .02                   0                   0                   0
#            sig_2yc                b_2c                n_2c           sig_2maxc                c_2c
                 160                   0                   0                 650                   0
#            EPS_1c2             EPS_2c2            sig_rsc2            Wpmax_c2
                 .03                   0                   0                   0
#            sig_12y                b_12                n_12           sig_12max                c_12
                  50                   0                   0                 100                   0
#           EPS_1_12            EPS_2_12           sig_rs_12            Wpmax_12
                   0                   0                   0                   0
#          GAMMA_ini           GAMMA_max              d3_max
                   0                   0                   0
#  Fsmooth                Fcut
         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. The formulation flag Iform should be set to 1, for the CRASURV (crash survivability) formulation. Compare with Iform=0, in this formulation:
    • The F variable coefficients of F(σ) MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacIcacqaHdpWCcaGGPaaaaa@39E0@ is function of plastic work and strain rate
    • It allows the simulation of the ductile failure of orthotropic shells
    • Considering different plastic and failure behaviors in tension, in compression and in shear
  2. Usage with property and element type.
    • This material requires orthotropic shell properties (/PROP/TYPE9 (SH_ORTH), /PROP/TYPE10 (SH_COMP) or /PROP/TYPE11 (SH_SANDW)). These properties specify the orthotropic direction, therefore, it is not compatible with the isotropic shell property (/PROP/TYPE1 (SHELL)). Property /PROP/SH_ORTH is not compatible with the CRASURV formulation.
    • This material is available with under-integrated Q4 (Ishell= 1,2,3,4) and fully integrated BATOZ (Ishell=12) shell formulations.
    • This material is compatible with orthotropic solid property (/PROP/SOL_ORTH), the orthotropic thick shell property (/PROP/TSH_ORTH) and the composite thick shell property (/PROP/TSH_COMP). These properties specify the orthotropic directions. It is assumed that, for solids and thick shells, the material is elastic and the E33 value must be set in such cases.
    • Failure criterion in LAW25 is not applicable to solid elements. To determine failure for solid elements /FAIL card should be used.
    • For shell and thick shell composite parts, with /PROP/SH_COMP, /PROP/SH_SANDW, /PROP/TSH_ORTH or /PROP/TSH_COMP, material is defined directly in the property card. The failure criteria defined within this material (for example, LAW25) are accounted for. Material referred to in the corresponding /PART card is not used.
  3. The Tsai-Wu criterion:
    The material is assumed to be elastic until the Tsai-Wu criterion is fulfilled:
    • If F(σ)<1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacIcacqaHdpWCcaGGPaGaeyipaWJaaGymaaaa@3B9F@ : Elastic
    • If F(σ)>1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacIcacqaHdpWCcaGGPaGaeyOpa4JaaGymaaaa@3BA3@ : Nonlinear
    Where, F(σ) MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacIcacqaHdpWCcaGGPaaaaa@39E0@ is stress in element for Tsai-Wu criterion, is computed as:(1)
    F(σ)=F1σ1+F2σ2+F11σ12+F22σ22+2F12σ1σ2+F44σ122 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbc9v8qqaqFr0xb9pg0xb9qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=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@6794@

    Here, σ1 , σ2 and σ12 are the stresses in the material coordinate system.

    The F variable coefficients of F(σ) MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacIcacqaHdpWCcaGGPaaaaa@39E0@ for Tsai-Wu criterion is functions of plastic work F(Wp*·ε˙) MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaOqaaiGacAeadaqadaqaaiaadEfadaqhaaWcbaGaamiCaaqaaiaacQcaaaGccqWIpM+zcuaH1oqzgaGaaaGaayjkaiaawMcaaaaa@426A@ and is determined as:(2)
    Fi(Wp*,ε˙)=1σic(Wp*,ε˙)+1σit(Wp*,ε˙)
    (3)
    Fii(Wp*,ε˙)=1σic(Wp*,ε˙)σit(Wp*,ε˙)
    (4)
    F12(Wp*,ε˙)=α2F11(Wp*,ε˙)F22(Wp*,ε˙)
    (5)
    F44(Wp*,ε˙)=1σ12(Wp*,ε˙)σ12(Wp*,ε˙)

    Where, i MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E4@ =1 or 2.

    The values of the limiting stresses when the material becomes nonlinear in directions 1, 2 or 12 (shear) are modified based on the values of plastic work and strain rate, as:

    In tension:(6)
    σit(Wp*,ε˙)=σiyt(1+bit(Wp*)nit)(1+citln(ε˙ε˙0))

    Where, i MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E4@ =1 or 2.

    In compression:(7)
    σic(Wp*,ε˙)=σiyc(1+bic(Wp*)nic)(1+cicln(ε˙ε˙0))

    Where, i MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E4@ =1 or 2.

    In shear:(8)
    σ12(Wp*,ε˙)=σ12y(1+b12(Wp*)n12)(1+c12ln(ε˙ε˙0))

    The superscripts c MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaSqaaiaadogaaaa@3A28@ and t MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaSqaaiaadogaaaa@3A28@ represent compression and tension, respectively.

    Plastic work Wp* MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaaiOkaaaaaaa@3B58@ in above limiting stress is defined as:(9)
    Wp*=WpWpref MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaOqaaiaadEfadaqhaaWcbaGaamiCaaqaaiaacQcaaaGccqGH9aqpdaWcaaqaaiaadEfadaWgaaWcbaGaamiCaaqabaaakeaacaWGxbWaa0baaSqaaiaadchaaeaacaWGYbGaamyzaiaadAgaaaaaaaaa@43DC@

    Where, Wpref MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaOqaaiaadEfadaqhaaWcbaGaamiCaaqaaiaadkhacaWGLbGaamOzaaaaaaa@3E09@ is unit reference plastic work per volume.

    This criterion represents a second order closed three-dimensional Tsai-Wu surface in σ1 , σ2 and σ12 space. This surface is scaled, moved and rotated due to the variation of plastic work and true strain rate.
    Note: For shear, the parameters determining nonlinear behavior are the same in tension and compression.
  4. Damage with tensile strain and energy failure.
    This material could describe in plane and out-of-plane damage.
    • In plane damage with damage factor di MathType@MTEF@5@5@+=feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsgadaWgaaWcbaGaamyAaaqabaaaaa@37EF@

      Global tensile strain damage between εti and εfi controlled by the damage factor di , which is given by:

      di=min(εiεtiεiεmiεmiεti, dmax) in directions, i = 1, 2

    • E-modulus
      E-modulus is reduced according to damage parameter if, εtiεiεfi MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aaSbaaSqaaiaadshacaWGPbaabeaakiabgsMiJkabew7aLnaaBaaaleaacaWGPbaabeaakiabgsMiJkabew7aLnaaBaaaleaacaWGMbGaamyAaaqabaaaaa@471B@ :(10)
      Eiireduced=Eii(1di) MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadweadaqhaaWcbaGaamyAaiaadMgaaeaacaWGYbGaamyzaiaadsgacaWG1bGaam4yaiaadwgacaWGKbaaaOGaeyypa0JaamyramaaBaaaleaacaWGPbGaamyAaaqabaGccaGGOaGaaGymaiabgkHiTiaadsgadaWgaaWcbaGaamyAaaqabaGccaGGPaaaaa@4837@
      E-modulus is reduced according to damage paramter, if εi>εfi MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aaSbaaSqaaiaadMgaaeqaaOGaeyOpa4JaeqyTdu2aaSbaaSqaaiaadAgacaWGPbaabeaaaaa@40F5@ :(11)
      Eiireduced=Eii(1dmax) MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadweadaqhaaWcbaGaamyAaiaadMgaaeaacaWGYbGaamyzaiaadsgacaWG1bGaam4yaiaadwgacaWGKbaaaOGaeyypa0JaamyramaaBaaaleaacaWGPbGaamyAaaqabaGccaGGOaGaaGymaiabgkHiTiaadsgadaWgaaWcbaGaciyBaiaacggacaGG4baabeaakiaacMcaaaa@4A1D@

      In this case, damage is set to dmax MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsgadaWgaaWcbaGaciyBaiaacggacaGG4baabeaaaaa@39D4@ and it is not updated further.

    • Yield Stress
      Yield stress is reduced since below damage strain in different loading:
      • εit1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aa0baaSqaaiaadMgaaeaacaqG0bGaaeymaaaaaaa@3DE3@ and εit2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aa0baaSqaaiaadMgaaeaacaWG0bGaaGOmaaaaaaa@3DED@ in tension
      • εic1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aa0baaSqaaiaadMgaaeaacaqGJbGaaeymaaaaaaa@3DD2@ and εic2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aa0baaSqaaiaadMgaaeaacaWGJbGaaGOmaaaaaaa@3DDC@ in compression
      • ε121 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aa0baaSqaaiaaigdacaaIYaaabaGaaeymaaaaaaa@3D75@ and ε122 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aa0baaSqaaiaaigdacaaIYaaabaGaaGOmaaaaaaa@3D7D@ in shear
      For example, tensile in direction 1 will be reduced when σ1maxt MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4Wdm3aa0baaSqaaiaaigdaciGGTbGaaiyyaiaacIhaaeaacaWG0baaaaaa@3FEE@ at εit1 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aa0baaSqaaiaadMgaaeaacaqG0bGaaeymaaaaaaa@3DE3@ and until residual stress σ1rst MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4Wdm3aa0baaSqaaiaaigdacaWGYbGaam4Caaqaaiaadshaaaaaaa@3F09@ at ε1t2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aa0baaSqaaiaaigdaaeaacaWG0bGaaGOmaaaaaaa@3DBA@ .


      Figure 1. Tensile in Direction 1
    • Element deletion is controlled by the Ioff flag.

    Out-of-plane damage (delamination) with γ .

    The simpliest delamination criterion is based on the evaluation of out-of-plane shear strains ( γ31 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEeek0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4SdC2aaSbaaSqaaiaaiodacaaIXaaabeaaaaa@3CC8@ and γ23 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEeek0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4SdC2aaSbaaSqaaiaaiodacaaIXaaabeaaaaa@3CC8@ ) with γ=(γ13)2+(γ23)2 MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=HhbHc9v8qqaqFr0xb9pg0xb9qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiaaciWacmaadaGabiaaeaGaauaaaOqaaiabeo7aNjabg2da9maakaaabaGaaiikaiabeo7aNnaaBaaaleaacaaIXaGaaG4maaqabaGccaGGPaWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaiikaiabeo7aNnaaBaaaleaacaaIYaGaaG4maaqabaGccaGGPaWaaWbaaSqabeaacaaIYaaaaaqabaaaaa@4928@ .
    • Element stresses and are gradually reduced if, γmax>γ>γini MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaGccqGH+aGpcqaHZoWzcqGH+aGpcqaHZoWzdaWgaaWcbaGaamyAaiaad6gacaWGPbaabeaaaaa@4300@
    • The element is completely removed (fails), if γγiniγmaxγini>d3max MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaOqaamaalaaabaGaeq4SdCMaeyOeI0Iaeq4SdC2aaSbaaSqaaiaadMgacaWGUbGaamyAaaqabaaakeaacqaHZoWzdaWgaaWcbaGaciyBaiaacggacaGG4baabeaakiabgkHiTiabeo7aNnaaBaaaleaacaWGPbGaamOBaiaadMgaaeqaaaaakiabg6da+iaadsgadaWgaaWcbaGaaG4maiGac2gacaGGHbGaaiiEaaqabaaaaa@5087@ in one of the shell layers.
  5. Element rupture with strain, damage and energy failure criterion.
    • Element rupture (stress set to zero) depends on the option WP_fail where either theglobal maximum plastic work Wpmax MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaciyBaiaacggacaGG4baaaaaa@3E48@ or directional maximum plastic work Wijpmax MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGPbGaamOAaiaadchaaeaaciGGTbGaaiyyaiaacIhaaaaaaa@4025@ will be taken into account. When the stress value of all layers is zero, the element is deleted.
      If WP_fail=0
      If the residual stress is greater than yield stress ( σrs>σy MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4Wdm3aaSbaaSqaaiaadkhacaWGZbaabeaakiabg6da+iabeo8aZnaaBaaaleaacaWG5baabeaaaaa@4153@ ), then the element layer ruptures (stress set to zero) if it reaches the directional maximum plastic work Wijpmax MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGPbGaamOAaiaadchaaeaaciGGTbGaaiyyaiaacIhaaaaaaa@4025@ . Example, tensile loading in direction 1 with σ1rst>σ1yt MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4Wdm3aa0baaSqaaiaaigdacaWGYbGaam4CaaqaaiaadshaaaGccqGH+aGpcqaHdpWCdaqhaaWcbaGaaGymaiaadMhaaeaacaWG0baaaaaa@44BD@ , element layer ruptured if plastic work reach W1pmaxt MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaWcdaqfGaqabeqabaGaamiDaaqaaiaabEfadaqhaaqaaWGaaeymaSGaamiCaaqaaiGac2gacaGGHbGaaiiEaaaaaaaaaa@4048@ .


      Figure 2.
      If the residual stress is not greater than yield stress ( σrsσy MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4Wdm3aaSbaaSqaaiaadkhacaWGZbaabeaakiabgsMiJkabeo8aZnaaBaaaleaacaWG5baabeaaaaa@4200@ ), then the element layer ruptures if it reaches the global maximum plastic work Wpmax MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaciyBaiaacggacaGG4baaaaaa@3E48@ . Example, tensile loading in direction 2 with σ2rstσ2yt MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeq4Wdm3aa0baaSqaaiaaikdacaWGYbGaam4CaaqaaiaadshaaaGccqGHKjYOcqaHdpWCdaqhaaWcbaGaaGOmaiaadMhaaeaacaWG0baaaaaa@456C@ , element layer ruptured if plastic work reach Wpmax MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaciyBaiaacggacaGG4baaaaaa@3E48@ .


      Figure 3.
      If WP_fail=1
      The element layer ruptures when it reaches the directional maximum plastic work in its direction Wijpmax MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGPbGaamOAaiaadchaaeaaciGGTbGaaiyyaiaacIhaaaaaaa@4025@ even if the residual stress is less than the yield stress.
    • Element deletion is controlled by the option Ioff which uses the following criteria or combinations of criteria.
      • Element rupture could be due to reaching the strain criterion ( εi>εmi MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaeqyTdu2aaSbaaSqaaiaadMgaaeqaaOGaeyOpa4tbaeqabeqaaaqaaiabew7aLnaaBaaaleaaciGGTbGaamyAaaqabaaaaaaa@40E8@ in direction i MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E4@ )
      • Damage criterion ( di>dmax MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=LipeYth9vqqj=hEeei0xXdbba9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0FirpepesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaamizamaaBaaaleaacaWGPbaabeaakiabg6da+uaabeqabeaaaeaacaWGKbWaaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaaaa@405F@ in direction i MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E4@ )
      • Plastic work failure criterion
      Note:
      • When using the plastic work failure criterion WP_fail, if a directional maximum plastic work is not entered, then the global maximum plastic strain will be taken.
      • Similarly, when ICCglobal=4, the global maximum plastic work or directional maximum plastic work will be scaled based on strain rate.
        For example, with a tensile loading in direction 2, the maximum plastic work values are scaled:(12)
        Wpmax(1+clnε˙2ε˙0) MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGxbWaa0baaSqaaiaadchaaeaaciGGTbGaaiyyaiaacIhaaaGccqGHflY1daqadaqaaiaaigdacqGHRaWkcaWGJbGaciiBaiaac6gadaWcaaqaaiqbew7aLzaacaWaaSbaaSqaaiaaikdaaeqaaaGcbaGafqyTduMbaiaadaWgaaWcbaGaaGimaaqabaaaaaGccaGLOaGaayzkaaaaaa@49D1@
        and(13)
        W2pmaxt(1+c2tlnε˙2ε˙0) MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGxbWaa0baaSqaaiaaikdacaWGWbaabaGaciyBaiaacggacaGG4bWaaWbaaWqabeaajugWaiaadshaaaaaaOGaeyyXIC9aaeWaaeaacaaIXaGaey4kaSIaam4yamaaDaaaleaacaaIYaaabaGaamiDaaaakiGacYgacaGGUbWaaSaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIYaaabeaaaOqaaiqbew7aLzaacaWaaSbaaSqaaiaaicdaaeqaaaaaaOGaayjkaiaawMcaaaaa@4ECE@
  6. The ratio field can be used to provide stability to composite shell components. For example, it allows you to delete unstable elements wherein, all but one layer has failed. This last layer may cause instability during simulation due to a low stiffness value. This option is available for strain and plastic energy based brittle failure.
  7. Tensile strain and energy failure criterion of LAW25 is not available for orthotropic shells with /PROP/TYPE9.
  8. The unit of Wpref MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaaaa@3D76@ is energy per unit of volume. If set Wpref MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaaaa@3D76@ as default value (0) is encountered, the default value is 1 unit of the model.
    Example:
    • If unit system of kg-m-s used in model, then Wpref=1[Jm3] MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaOGaeyypa0JaaGymamaadmaabaWaaSaaaeaacaGGkbaabaGaaiyBamaaCaaaleqabaGaai4maaaaaaaakiaawUfacaGLDbaaaaa@43F0@
    • If unit system of Ton-mm-s used in model, then Wpref=1[mJmm3] MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaOGaeyypa0JaaGymamaadmaabaWaaSaaaeaacaGGTbGaaiOsaaqaaiaac2gacaGGTbWaaWbaaSqabeaacaGGZaaaaaaaaOGaay5waiaaw2faaaaa@45D2@
    For proper conversion of this value if changing units in pre- and post-processor, it is advised to replace the default value by the true value “1”, so that the value of Wpref MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaaaa@3D76@ will be automatically converted. Leaving the Wpref MathType@MTEF@5@5@+=feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhiov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yqaiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcbaGaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaaaa@3D76@ field to “0” may result in errors in case of automatic conversion.
    Note: A local unit system can be created for the material to avoid conversion.
  9. Output for post-processing:
    • To post-process this material in the animation file, the following Engine cards should be used:
      • /ANIM/SHELL/WPLA/ALL for plastic work output
      • /ANIM/BRICK/WPLA for plastic work output
      • /ANIM/SHELL/TENS/STRAIN for strain tensor output in the elemental coordinate system
      • /ANIM/SHELL/TENS/STRESS for stress tensor output in the elemental coordinate system
      • /ANIM/SHELL/PHI angle between elemental and first material direction
      • /ANIM/SHELL/FAIL number of failed layers.
    • To post-process this material in the time-history file, the following definitions in /TH/SHEL or /TH/SH3N card should be used:
      • PLAS (or EMIN and EMAX) for minimum and maximum plastic work in the shell.
      • WPLAYJJ (JJ=0 to 99) for plastic work in a corresponding layer.
    • The output file (*0001.out) displays some information when the failure criteria is met:
      • Failure 1 and 2 means tensile failure direction 1 or 2, respectively
      • Failure -P means global plastic work failure
      • P-T1 / P-T2 means plastic work failure in tension direction 1 or 2, respectively
      • P-C1 / P-C2 means plastic work failure in compression direction 1 or 2, respectively
      • P-T12 means plastic work failure in shear

      The failure message also indicates which element and which layer is affected. It is output when the failure criteria is met for an integration point. As Batoz elements have 4 integrations points for each layer, this message may be output up to 4 times per layer and elements in this case.

  10. /VISC/PRONY can be used with this material law to include viscous effects.