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
ρ i                
E11 E22 ν 12 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyVd42aaSbaaSqaaiaaigdacaaIYaaabeaaaaa@3CD1@ Iform   E33
G12 G23 G31 ε f 1 ε f 2
ε t 1 ε m 1 ε t 2 ε m 2 dmax
Composite Plasticity Hardening
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
W p max   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)
σ 1 y t b 1 t n 1 t σ 1 max t c 1 t
ε 1 t 1 ε 1 t 2 σ 1 r s t W 1 p max t    
σ 2 y t b 2 t n 2 t σ 2 max t c 2 t
ε 2 t1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aa0baaSqaaiaaikdaaeaacaWG0bGaaGymaaaaaaa@3DBA@ ε 2 t 2 σ 2 r s t W 2p max t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba WcdaqfGaqabeqabaGaamiDaaqaaiaabEfadaqhaaqaaWGaaeOmaSGa amiCaaqaaiGac2gacaGGHbGaaiiEaaaaaaaaaa@4049@    
Composite Plasticity in Compression Directions 1 and 2
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
σ 1 y c b 1 c n 1 c σ 1 max c c 1 c
ε 1 c 1 ε 1 c 2 σ 1rs c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4Wdm3aa0baaSqaaiaabgdacaWGYbGaam4Caaqaaiaadogaaaaa aa@3EF1@ W 1 p max c    
σ 2 y c b 2 c n 2 c σ 2 max c c 2 c
ε 2 c 1 ε 2 c 2 σ 2rs c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4Wdm3aa0baaSqaaiaabkdacaWGYbGaam4Caaqaaiaadogaaaaa aa@3EF2@ W 2 p max c    
Composite Plasticity in Shear
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
σ 12 y b 12 n 12 σ 12 max c 12
ε 1 2 1 ε 1 2 2 σ 12 r s W 12 p max    
Delamination
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
γ i n i γ max 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)

 
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 ]
ν 12 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyVd42aaSbaaSqaaiaaigdacaaIYaaabeaaaaa@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 ]
ε f 1 Maximum tensile strain for element deletion in material direction 1.

Default = 1.2 x 1020 (Real)

ε f 2 Maximum tensile strain for element deletion in material direction 2.

Default = 1.2 x 1020 (Real)

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

Default = 1.0 x 1020 (Real)

ε m 1 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)

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

Default = 1.0 x 1020 (Real)

ε m 2 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)

W p max Global maximum plastic work per unit shell volume.

Default = 1020 (Real)

[ J m 3 ]
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, Condition 1:{ either max. plastic work reached or ε 1 > ε m1 in direction 1 or d 1 > d max in direction 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qaiaad+gacaWGUbGaamizaiaadMgacaWG0bGaamyAaiaad+ga caWGUbGaaGjbVxaabeqabeaaaeaaaaGaaGymaiaacQdadaGabaqaau aabeqadeaaaeaacaWGLbGaamyAaiaadshacaWGObGaamyzaiaadkha faqabeqabaaabaaaaiaaysW7ciGGTbGaaiyyaiaacIhacaGGUaqbae qabeqaaaqaaaaacaaMe8UaamiCaiaadYgacaWGHbGaam4Caiaadsha caWGPbGaam4yauaabeqabeaaaeaaaaGaaGzaVlaaysW7caWG3bGaam 4BaiaadkhacaWGRbqbaeqabeqaaaqaaaaacaaMe8UaamOCaiaadwga caWGHbGaam4yaiaadIgacaWGLbGaamizaaqaauaabeqabeaaaeaaaa qbaeqabeqaaaqaaaaacaWGVbGaamOCauaabeqabeaaaeaaaaqbaeqa beqaaaqaaaaacaaMe8UaeqyTdu2aaSbaaSqaaiaaigdaaeqaaOGaey Opa4tbaeqabeqaaaqaaiabew7aLnaaBaaaleaaciGGTbGaaGymaaqa baGcfaqabeqabaaabaaaaiaaysW7caaMe8UaamyAaiaad6gafaqabe qabaaabaaaaiaaysW7caWGKbGaamyAaiaadkhacaWGLbGaam4yaiaa dshacaWGPbGaam4Baiaad6gafaqabeqabaaabaaaaiaaigdaaaaaba qbaeqabeqaaaqaaaaafaqabeqabaaabaaaaiaad+gacaWGYbqbaeqa beqaaaqaaaaafaqabeqabaaabaaaaiaaysW7caWGKbWaaSbaaSqaai aaigdaaeqaaOGaeyOpa4tbaeqabeqaaaqaaiaadsgadaWgaaWcbaGa ciyBaiaacggacaGG4baabeaakuaabeqabeaaaeaaaaGaaGjbVlaays W7caWGPbGaamOBauaabeqabeaaaeaaaaGaaGjbVlaadsgacaWGPbGa amOCaiaadwgacaWGJbGaamiDaiaadMgacaWGVbGaamOBauaabeqabe aaaeaaaaGaaGymaaaaaaaacaGL7baaaaa@9CCE@
= 3
Shell is deleted if for each element layer, Condition 2:{ either max. plastic work reached or ε 2 > ε m2 in direction 2 or d 2 > d max in direction 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4qaiaad+gacaWGUbGaamizaiaadMgacaWG0bGaamyAaiaad+ga caWGUbqbaeqabeqaaaqaaaaacaaMe8UaaGOmaiaacQdadaGabaqaau aabeqadeaaaeaacaWGLbGaamyAaiaadshacaWGObGaamyzaiaadkha faqabeqabaaabaaaaiaaygW7caaMe8UaaGjbVlGac2gacaGGHbGaai iEaiaac6cafaqabeqabaaabaaaaiaaysW7caWGWbGaamiBaiaadgga caWGZbGaamiDaiaadMgacaWGJbqbaeqabeqaaaqaaaaacaaMe8Uaam 4Daiaad+gacaWGYbGaam4AauaabeqabeaaaeaaaaGaaGjbVlaadkha caWGLbGaamyyaiaadogacaWGObGaamyzaiaadsgaaeaafaqabeqaba aabaaaauaabeqabeaaaeaaaaGaam4Baiaadkhafaqabeqabaaabaaa auaabeqabeaaaeaaaaGaaGjbVlabew7aLnaaBaaaleaacaaIYaaabe aakiabg6da+uaabeqabeaaaeaacqaH1oqzdaWgaaWcbaGaamyBaiaa ikdaaeqaaOqbaeqabeqaaaqaaaaacaaMe8UaamyAaiaad6gafaqabe qabaaabaaaaiaaysW7caaMe8UaamizaiaadMgacaWGYbGaamyzaiaa dogacaWG0bGaamyAaiaad+gacaWGUbqbaeqabeqaaaqaaaaacaaIYa aaaaqaauaabeqabeaaaeaaaaqbaeqabeqaaaqaaaaacaWGVbGaamOC auaabeqabeaaaeaaaaqbaeqabeqaaaqaaaaacaaMe8UaamizamaaBa aaleaacaaIYaaabeaakiabg6da+uaabeqabeaaaeaacaWGKbWaaSba aSqaaiGac2gacaGGHbGaaiiEaaqabaGcfaqabeqabaaabaaaaiaays W7caWGPbGaamOBauaabeqabeaaaeaaaaGaaGjbVlaaysW7caWGKbGa amyAaiaadkhacaWGLbGaam4yaiaadshacaWGPbGaam4Baiaad6gafa qabeqabaaabaaaaiaaikdaaaaaaaGaay5Eaaaaaa@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 W i j p max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGxbWaa0 baaSqaaiaadMgacaWGQbGaamiCaaqaaiGac2gacaGGHbGaaiiEaaaa aaa@3E17@ defines rupture only if residual stress greater than yield stress. Otherwise, global maximum plastic work W p max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba WccaWGxbaddaqhaaqaaiaadchaaeaaciGGTbGaaiyyaiaacIhaaaaa aa@3E54@ defines rupture.
=1
Directional maximum plastic work W i j p max MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGxbWaa0 baaSqaaiaadMgacaWGQbGaamiCaaqaaiGac2gacaGGHbGaaiiEaaaa aaa@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 n u m b e r o f f a i l e d l a y e r s n u m b e r o f t o t a l l a y e r s r a t i o .

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)

[ 1 s ]
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 σ 1 max t , σ 2 max t , σ 1 max c , σ 2 max c , σ 12 max is taken into account, but there is no strain rate effect on W p max
= 2
No strain rate effect on σ 1 max t , σ 2 max t , σ 1 max c , σ 2 max c , σ 12 max and W p max .
= 3
Strain rate effect on σ 1 max t , σ 2 max t , σ 1 max c , σ 2 max c , σ 12 max is taken into account, but there is no strain rate effect on W p max .
= 4
Strain rate effect on W p max is taken into account, but there is no strain rate effect on σ 1 max t , σ 2 max t , σ 1 max c , σ 2 max c , σ 12 max .

(Integer)

σ 1 y t Yield stress in tension in direction 1.

Default = 0.0 (Real)

[ Pa ]
b 1 t Plastic hardening parameter in tension in direction 1.

Default = 0.0 (Real)

n 1 t Plastic hardening exponent in tension in direction 1.

Default = 1.0 (Real)

σ 1 max t Maximum stress in tension in direction 1.

Default = 1020 (Real)

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

Default = c (Real)

ε 1 t 1 Initial softening strain in tension in the material direction 1.

Default = 1.0 x 1020 (Real)

ε 1 t 2 Maximum softening strain in tension in the material direction 1.

Default = 1.2 ε 1 t 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaaigdaaeaacaWG 0bGaaGymaaaaaaa@3FE2@ (Real)

σ 1 r s t Residual stress in tension in direction 1.

Default = 10 3 σ 1 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWC daqhaaWcbaGaaGymaiaadMhaaeaacaWG0baaaaaa@416E@ (Real)

[ Pa ]
W 1 p max t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba WcdaqfGaqabeqabaGaamiDaaqaaiaabEfadaqhaaqaaWGaaeymaSGa amiCaaqaaiGac2gacaGGHbGaaiiEaaaaaaaaaa@4048@ Directional maximum plastic work per unit shell volume in tension in direction 1. 4

Default = 1020 (Real)

[ J m 3 ]
σ 2 y t Yield stress in tension in direction 2.

Default = 0.0 (Real)

[ Pa ]
b 2 t Plastic hardening parameter in tension in direction 2.

Default = 0.0 (Real)

n 2 t Plastic hardening exponent in tension in direction 2.

Default = 1.0 (Real)

σ 2 max t Maximum stress in tension in direction 2.

Default = 1020 (Real)

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

Default = c (Real)

ε 2 t 1 Initial softening strain in tension in the material direction 2.

Default = 1.0 x 1020 (Real)

ε 2 t 2 Maximum softening strain in tension in direction 2.

Default = 1.2 ε 1 t 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaaigdaaeaacaWG 0bGaaGOmaaaaaaa@3FE3@ (Real)

σ 2 r s t Residual stress in tension in direction 2.

Default = 10 3 σ 2 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWC daqhaaWcbaGaaGOmaiaadMhaaeaacaWG0baaaaaa@416F@ (Real)

[ Pa ]
W 2 p max t Directional maximum plastic work per unit shell volume in tension in direction 2. 4

Default = 1020 (Real)

[ J m 3 ]
σ 1 y c Yield stress in compression in direction 1.

Default = 0.0 (Real)

[ Pa ]
b 1 c Plastic hardening parameter in compression in direction 1.

Default = b 2 t (Real)

n 1 c Plastic hardening exponent in compression in direction 1.

Default = n 2 t (Real)

σ 1 max c Maximum stress in compression in direction 1.

Default = 1020 (Real)

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

Default = c (Real)

ε 1 c 1 Initial softening strain in compression in the material direction 1.

Default = 1.0 x 1020 (Real)

ε 1 c 2 Maximum softening strain in compression in the material direction 1.

Default = 1.2 ε 1 c 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaaigdaaeaacaWG JbGaaGymaaaaaaa@3FD1@ (Real)

σ 1 r s c Residual stress in compression in direction 1.

Default = 10 3 σ 1 y c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWC daqhaaWcbaGaaGymaiaadMhaaeaacaWGJbaaaaaa@415D@ (Real)

[ Pa ]
W 1 p max c Directional maximum plastic work per unit shell volume in compression in direction 1.

Default = 1020 (Real)

[ J m 3 ]
σ 2 y c Yield stress in compression in direction 2.

Default = 0.0 (Real)

[ Pa ]
b 2 c Plastic hardening parameter in compression in direction 2.

Default = b 2 t (Real)

n 2 c Plastic hardening exponent in compression in direction 2.

Default = n 2 t (Real)

σ 2 max c Maximum stress in compression in direction 2.

Default = 1020 (Real)

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

Default = c (Real)

ε 2 c 1 Initial softening strain in compression in the material direction 2.

Default = 1.0 x 1020 (Real)

ε 2 c 2 Maximum softening strain in compression in the material direction 2.

Default = 1.2 ε 2 c 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaabkdaaeaacaWG JbGaaeymaaaaaaa@3FC4@ (Real)

σ 2 r s c Residual stress in compression in direction 2.

Default = 10 3 σ 2 y c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWC daqhaaWcbaGaaGOmaiaadMhaaeaacaWGJbaaaaaa@415E@ (Real)

[ Pa ]
W 2 p max c Directional maximum plastic work per unit shell volume in compression in direction 2. 4

Default = 1020 (Real)

[ J m 3 ]
σ 12 y Yield stress in direction 12 (in 45 degree of fiber direction).

Default = 0.0 (Real)

[ Pa ]
b 12 Plastic hardening parameter in direction 12.

Default = b 2 t (Real)

n 12 Plastic hardening exponent in direction 12.

Default = n 2 t (Real)

σ 12 max Maximum stress in direction 12.

Default = 1020 (Real)

[ Pa ]
ε 1 2 1 Strain rate coefficient in direction 12.
= 0
No strain rate dependency.

Default = c (Real)

ε 1 2 1 Initial softening strain in the material direction 12.

Default = 1.0 x 1020 (Real)

ε 1 2 2 Maximum softening strain in the material direction 12.

Default = 1.2 ε 1 2 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaac6cacaaIYaGaeqyTdu2aa0baaSqaaiaaigdacaqGYaaa baGaaGymaaaaaaa@3F9E@ (Real)

σ 12 r s Residual stress in direction 12.

Default = 10 3 σ 12 y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaaGymaiaaicdadaahaaWcbeqaaiabgkHiTiaaiodaaaGccqaHdpWC daWgaaWcbaGaaGymaiaaikdacaWG5baabeaaaaa@4130@ (Real)

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

Default = 1020 (Real)

[ J m 3 ]
γ ini Out of plane shear strain when delamination begins. 4

Default = 1020 (Real)

γ max 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@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacqaHdpWCcaGGPaaaaa@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@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacqaHdpWCcaGGPaGaeyipaWJaaGymaaaa@3B9F@ : Elastic
    • If F ( σ ) > 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacqaHdpWCcaGGPaGaeyOpa4JaaGymaaaa@3BA3@ : Nonlinear
    Where, F ( σ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacqaHdpWCcaGGPaaaaa@39E0@ is stress in element for Tsai-Wu criterion, is computed as:(1)
    F ( σ ) = F 1 σ 1 + F 2 σ 2 + F 11 σ 1 2 + F 22 σ 2 2 + 2 F 12 σ 1 σ 2 + F 44 σ 12 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbc9v8 qqaqFr0xb9pg0xb9qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs 0dXdHuk9fr=xfr=xfrpeWZqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiGacAeaciGGOaGaeq4WdmNaaiykaiabg2da9iaadAeadaWgaaWc baGaaGymaaqabaGccqaHdpWCdaWgaaWcbaGaaGymaaqabaGccqGHRa WkcaWGgbWaaSbaaSqaaiaaikdaaeqaaOGaeq4Wdm3aaSbaaSqaaiaa ikdaaeqaaOGaey4kaSIaamOramaaBaaaleaacaaIXaGaaGymaaqaba GccqaHdpWCdaqhaaWcbaGaaGymaaqaaiaaikdaaaGccqGHRaWkcaWG gbWaaSbaaSqaaiaaikdacaaIYaaabeaakiabeo8aZnaaDaaaleaaca aIYaaabaGaaGOmaaaakiabgUcaRiaaikdacaWGgbWaaSbaaSqaaiaa igdacaaIYaaabeaakiabeo8aZnaaBaaaleaacaaIXaaabeaakiabeo 8aZnaaBaaaleaacaaIYaaabeaakiabgUcaRiaadAeadaWgaaWcbaGa aGinaiaaisdaaeqaaOGaeq4Wdm3aa0baaSqaaiaaigdacaaIYaaaba GaaGOmaaaaaaa@6794@

    Here, σ 1 , σ 2 and σ 12 are the stresses in the material coordinate system.

    The F variable coefficients of F ( σ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciOraiGacI cacqaHdpWCcaGGPaaaaa@39E0@ for Tsai-Wu criterion is functions of plastic work F ( W p * · ε ˙ ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiGacAeadaqadaqaaiaadEfadaqhaaWcbaGaamiCaaqaaiaacQca aaGccqWIpM+zcuaH1oqzgaGaaaGaayjkaiaawMcaaaaa@426A@ and is determined as:(2)
    F i ( W p * , ε ˙ ) = 1 σ i c ( W p * , ε ˙ ) + 1 σ i t ( W p * , ε ˙ )
    (3)
    F i i ( W p * , ε ˙ ) = 1 σ i c ( W p * , ε ˙ ) σ i t ( W p * , ε ˙ )
    (4)
    F 12 ( W p * , ε ˙ ) = α 2 F 11 ( W p * , ε ˙ ) F 22 ( W p * , ε ˙ )
    (5)
    F 44 ( W p * , ε ˙ ) = 1 σ 12 ( W p * , ε ˙ ) σ 12 ( W p * , ε ˙ )

    Where, i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=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)
    σ i t ( W p * , ε ˙ ) = σ i y t ( 1 + b i t ( W p * ) n i t ) ( 1 + c i t ln ( ε ˙ ε ˙ 0 ) )

    Where, i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E4@ =1 or 2.

    In compression:(7)
    σ i c ( W p * , ε ˙ ) = σ i y c ( 1 + b i c ( W p * ) n i c ) ( 1 + c i c ln ( ε ˙ ε ˙ 0 ) )

    Where, i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E4@ =1 or 2.

    In shear:(8)
    σ 12 ( W p * , ε ˙ ) = σ 12 y ( 1 + b 12 ( W p * ) n 12 ) ( 1 + c 12 ln ( ε ˙ ε ˙ 0 ) )

    The superscripts c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaS qaaiaadogaaaa@3A28@ and t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaS qaaiaadogaaaa@3A28@ represent compression and tension, respectively.

    Plastic work W p * MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaaiOkaaaaaaa@3B58@ in above limiting stress is defined as:(9)
    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@

    Where, W p ref MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiaadEfadaqhaaWcbaGaamiCaaqaaiaadkhacaWGLbGaamOzaaaa aaa@3E09@ is unit reference plastic work per volume.

    This criterion represents a second order closed three-dimensional Tsai-Wu surface in σ 1 , σ 2 and σ 12 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 d i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsgadaWgaa WcbaGaamyAaaqabaaaaa@37EF@

      Global tensile strain damage between ε t i and ε f i controlled by the damage factor d i , which is given by:

      d i = min ( ε i ε t i ε i ε m i ε m i ε t i ,   d max ) in directions, i = 1, 2

    • E-modulus
      E-modulus is reduced according to damage parameter if, ε t i ε i ε f i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aaSbaaSqaaiaadshacaWGPbaabeaakiabgsMiJkabew7a LnaaBaaaleaacaWGPbaabeaakiabgsMiJkabew7aLnaaBaaaleaaca WGMbGaamyAaaqabaaaaa@471B@ :(10)
      E i i r e d u c e d = E i i ( 1 d i ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadweadaqhaa WcbaGaamyAaiaadMgaaeaacaWGYbGaamyzaiaadsgacaWG1bGaam4y aiaadwgacaWGKbaaaOGaeyypa0JaamyramaaBaaaleaacaWGPbGaam yAaaqabaGccaGGOaGaaGymaiabgkHiTiaadsgadaWgaaWcbaGaamyA aaqabaGccaGGPaaaaa@4837@
      E-modulus is reduced according to damage paramter, if ε i > ε f i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aaSbaaSqaaiaadMgaaeqaaOGaeyOpa4JaeqyTdu2aaSba aSqaaiaadAgacaWGPbaabeaaaaa@40F5@ :(11)
      E i i r e d u c e d = E i i ( 1 d max ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadweadaqhaa WcbaGaamyAaiaadMgaaeaacaWGYbGaamyzaiaadsgacaWG1bGaam4y aiaadwgacaWGKbaaaOGaeyypa0JaamyramaaBaaaleaacaWGPbGaam yAaaqabaGccaGGOaGaaGymaiabgkHiTiaadsgadaWgaaWcbaGaciyB aiaacggacaGG4baabeaakiaacMcaaaa@4A1D@

      In this case, damage is set to d max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaiaadsgadaWgaa WcbaGaciyBaiaacggacaGG4baabeaaaaa@39D4@ and it is not updated further.

    • Yield Stress
      Yield stress is reduced since below damage strain in different loading:
      • ε i t1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aa0baaSqaaiaadMgaaeaacaqG0bGaaeymaaaaaaa@3DE3@ and ε i t 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aa0baaSqaaiaadMgaaeaacaWG0bGaaGOmaaaaaaa@3DED@ in tension
      • ε i c1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aa0baaSqaaiaadMgaaeaacaqGJbGaaeymaaaaaaa@3DD2@ and ε i c 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aa0baaSqaaiaadMgaaeaacaWGJbGaaGOmaaaaaaa@3DDC@ in compression
      • ε 12 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aa0baaSqaaiaaigdacaaIYaaabaGaaeymaaaaaaa@3D75@ and ε 12 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aa0baaSqaaiaaigdacaaIYaaabaGaaGOmaaaaaaa@3D7D@ in shear
      For example, tensile in direction 1 will be reduced when σ 1 max t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4Wdm3aa0baaSqaaiaaigdaciGGTbGaaiyyaiaacIhaaeaacaWG 0baaaaaa@3FEE@ at ε i t1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aa0baaSqaaiaadMgaaeaacaqG0bGaaeymaaaaaaa@3DE3@ and until residual stress σ 1 r s t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4Wdm3aa0baaSqaaiaaigdacaWGYbGaam4Caaqaaiaadshaaaaa aa@3F09@ at ε 1 t2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aa0baaSqaaiaaigdaaeaacaWG0bGaaGOmaaaaaaa@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 ( γ 31 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEeek0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4SdC2aaSbaaSqaaiaaiodacaaIXaaabeaaaaa@3CC8@ and γ 23 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=viVeYth9vqqj=hEeek0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4SdC2aaSbaaSqaaiaaiodacaaIXaaabeaaaaa@3CC8@ ) with γ = ( γ 13 ) 2 + ( γ 23 ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=HhbHc9v8 qqaqFr0xb9pg0xb9qqaqFn0dXdHiVcFbIOFHK8Feea0dXdar=Jb9hs 0dXdHuk9fr=xfr=xfrpeWZqaaiaaciWacmaadaGabiaaeaGaauaaaO qaaiabeo7aNjabg2da9maakaaabaGaaiikaiabeo7aNnaaBaaaleaa caaIXaGaaG4maaqabaGccaGGPaWaaWbaaSqabeaacaaIYaaaaOGaey 4kaSIaaiikaiabeo7aNnaaBaaaleaacaaIYaGaaG4maaqabaGccaGG PaWaaWbaaSqabeaacaaIYaaaaaqabaaaaa@4928@ .
    • Element stresses and are gradually reduced if, γ max > γ > γ i n i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4SdC2aaS baaSqaaiGac2gacaGGHbGaaiiEaaqabaGccqGH+aGpcqaHZoWzcqGH +aGpcqaHZoWzdaWgaaWcbaGaamyAaiaad6gacaWGPbaabeaaaaa@4300@
    • The element is completely removed (fails), if γ γ i n i γ max γ i n i > d 3 max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY=Hhbbf9v8 qqaqFr0xc9pk0xbba9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9 pgeaYRXxe9vr0=vr0=vqpWqaaiaaciWacmaadaGabiaaeaGaauaaaO qaamaalaaabaGaeq4SdCMaeyOeI0Iaeq4SdC2aaSbaaSqaaiaadMga caWGUbGaamyAaaqabaaakeaacqaHZoWzdaWgaaWcbaGaciyBaiaacg gacaGG4baabeaakiabgkHiTiabeo7aNnaaBaaaleaacaWGPbGaamOB aiaadMgaaeqaaaaakiabg6da+iaadsgadaWgaaWcbaGaaG4maiGac2 gacaGGHbGaaiiEaaqabaaaaa@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 W p max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaciyBaiaacggacaGG4baaaaaa @3E48@ or directional maximum plastic work W i j p max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGPbGaamOAaiaadchaaeaaciGGTbGaaiyy aiaacIhaaaaaaa@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 ( σ r s > σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4Wdm3aaSbaaSqaaiaadkhacaWGZbaabeaakiabg6da+iabeo8a ZnaaBaaaleaacaWG5baabeaaaaa@4153@ ), then the element layer ruptures (stress set to zero) if it reaches the directional maximum plastic work W i j p max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGPbGaamOAaiaadchaaeaaciGGTbGaaiyy aiaacIhaaaaaaa@4025@ . Example, tensile loading in direction 1 with σ 1 r s t > σ 1 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4Wdm3aa0baaSqaaiaaigdacaWGYbGaam4CaaqaaiaadshaaaGc cqGH+aGpcqaHdpWCdaqhaaWcbaGaaGymaiaadMhaaeaacaWG0baaaa aa@44BD@ , element layer ruptured if plastic work reach W 1 p max t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba WcdaqfGaqabeqabaGaamiDaaqaaiaabEfadaqhaaqaaWGaaeymaSGa amiCaaqaaiGac2gacaGGHbGaaiiEaaaaaaaaaa@4048@ .


      Figure 2.
      If the residual stress is not greater than yield stress ( σ r s σ y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4Wdm3aaSbaaSqaaiaadkhacaWGZbaabeaakiabgsMiJkabeo8a ZnaaBaaaleaacaWG5baabeaaaaa@4200@ ), then the element layer ruptures if it reaches the global maximum plastic work W p max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaciyBaiaacggacaGG4baaaaaa @3E48@ . Example, tensile loading in direction 2 with σ 2 r s t σ 2 y t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaeq4Wdm3aa0baaSqaaiaaikdacaWGYbGaam4CaaqaaiaadshaaaGc cqGHKjYOcqaHdpWCdaqhaaWcbaGaaGOmaiaadMhaaeaacaWG0baaaa aa@456C@ , element layer ruptured if plastic work reach W p max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaciyBaiaacggacaGG4baaaaaa @3E48@ .


      Figure 3.
      If WP_fail=1
      The element layer ruptures when it reaches the directional maximum plastic work in its direction W i j p max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8YjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGPbGaamOAaiaadchaaeaaciGGTbGaaiyy aiaacIhaaaaaaa@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 ( ε i > ε m i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaeqyTdu2aaSbaaSqaaiaadMgaaeqaaOGaeyOpa4tbaeqabeqaaaqa aiabew7aLnaaBaaaleaaciGGTbGaamyAaaqabaaaaaaa@40E8@ in direction i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyAaaaa@36E4@ )
      • Damage criterion ( d i > d max MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=LipeYth9vqqj=hEeei0xXdbb a9frFf0=yqFf0dbba91qpepeI8k8fiI+fsY=rqaqpepae9pg0Firpe pesP0xe9Fve9Fve9qapdbaGaaiGadiWaamaaceGaaqaacaqbaaGcba GaamizamaaBaaaleaacaWGPbaabeaakiabg6da+uaabeqabeaaaeaa caWGKbWaaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaaaaaaa@405F@ in direction i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=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)
        W p max ( 1 + c ln ε ˙ 2 ε ˙ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGxbWaa0 baaSqaaiaadchaaeaaciGGTbGaaiyyaiaacIhaaaGccqGHflY1daqa daqaaiaaigdacqGHRaWkcaWGJbGaciiBaiaac6gadaWcaaqaaiqbew 7aLzaacaWaaSbaaSqaaiaaikdaaeqaaaGcbaGafqyTduMbaiaadaWg aaWcbaGaaGimaaqabaaaaaGccaGLOaGaayzkaaaaaa@49D1@
        and(13)
        W 2 p max t ( 1 + c 2 t ln ε ˙ 2 ε ˙ 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqGqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGxbWaa0 baaSqaaiaaikdacaWGWbaabaGaciyBaiaacggacaGG4bWaaWbaaWqa beaajugWaiaadshaaaaaaOGaeyyXIC9aaeWaaeaacaaIXaGaey4kaS Iaam4yamaaDaaaleaacaaIYaaabaGaamiDaaaakiGacYgacaGGUbWa aSaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIYaaabeaaaOqaaiqbew 7aLzaacaWaaSbaaSqaaiaaicdaaeqaaaaaaOGaayjkaiaawMcaaaaa @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 W p r e f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaaaa @3D76@ is energy per unit of volume. If set W p r e f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaaaa @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 W p r e f = 1 [ J m 3 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaOGa eyypa0JaaGymamaadmaabaWaaSaaaeaacaGGkbaabaGaaiyBamaaCa aaleqabaGaai4maaaaaaaakiaawUfacaGLDbaaaaa@43F0@
    • If unit system of Ton-mm-s used in model, then W p r e f = 1 [ m J m m 3 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaOGa eyypa0JaaGymamaadmaabaWaaSaaaeaacaGGTbGaaiOsaaqaaiaac2 gacaGGTbWaaWbaaSqabeaacaGGZaaaaaaaaOGaay5waiaaw2faaaaa @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 W p r e f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaaaa @3D76@ will be automatically converted. Leaving the W p r e f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKf MBHbqefqvATv2CG4uz3bIuV1wyUbqedmvETj2BSbqefm0B1jxALjhi ov2DaebbnrfifHhDYfgasaacH8WjY=vipgYlh9vqqj=hEeeu0xXdbb a9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9q8qqaq=dir=f0=yq aiVgFr0xfr=xfr=xb9adbaGaaiGadiWaamaaceGaaqaacaqbaaGcba Gaam4vamaaDaaaleaacaWGWbaabaGaamOCaiaadwgacaWGMbaaaaaa @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.