CRASURV Formulation (I_form= 1)

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

Definitions

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 I_form should be set to 1, for the CRASURV (crash survivability) formulation. Compare with I_form=0, in this formulation:
   • The F variable coefficients of $\mathrm{F}(\sigma )$ 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 (I_shell= 1,2,3,4) and fully integrated BATOZ (I_shell=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 $\mathrm{F}(\sigma )<1$ : Elastic
   • If $\mathrm{F}(\sigma )>1$ : Nonlinear
   Where, $\mathrm{F}(\sigma )$ is stress in element for Tsai-Wu criterion, is computed as:(1)

   $$\mathrm{F}(\sigma )=F_1{\sigma }_1+F_2{\sigma }_2+F_{11}{\sigma }_1^2+F_{22}{\sigma }_2^2+2F_{12}{\sigma }_1{\sigma }_2+F_{44}{\sigma }_{12}^2$$

   Here, ${\sigma }_1$ , ${\sigma }_2$ and ${\sigma }_{12}$ are the stresses in the material coordinate system.

   The F variable coefficients of $\mathrm{F}(\sigma )$ for Tsai-Wu criterion is functions of plastic work $\mathrm{F}\left(W_p^{*}·\dot{\epsilon }\right)$ and is determined as:(2)

   $$F_i\left(W_p^{*},\dot{\epsilon }\right)=-\frac{1}{{\sigma }_i^c\left(W_p^{*},\dot{\epsilon }\right)}+\frac{1}{{\sigma }_i^t\left(W_p^{*},\dot{\epsilon }\right)}$$

   (3)

   $$F_{ii}\left(W_p^{*},\dot{\epsilon }\right)=\frac{1}{{\sigma }_i^c\left(W_p^{*},\dot{\epsilon }\right)\cdot {\sigma }_i^t\left(W_p^{*},\dot{\epsilon }\right)}$$

   (4)

   $$F_{12}\left(W_p^{*},\dot{\epsilon }\right)=-\frac{\alpha }{2}\sqrt{F_{11}\left(W_p^{*},\dot{\epsilon }\right)F_{22}\left(W_p^{*},\dot{\epsilon }\right)}$$

   (5)

   $$F_{44}\left(W_p^{*},\dot{\epsilon }\right)=\frac{1}{{\sigma }_{12}^{}\left(W_p^{*},\dot{\epsilon }\right)\cdot {\sigma }_{12}^{}\left(W_p^{*},\dot{\epsilon }\right)}$$

   Where, $i$ =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)

   $${\sigma }_i^t\left(W_p^{*},\dot{\epsilon }\right)\text{=}{\sigma }_{iy}^t\left(1+b_i^t{(W_p^{*})}^{n_i^t}\right)\left(1+c_i^t\ln \left(\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)\right)$$

   Where, $i$ =1 or 2.

   In compression:(7)

   $${\sigma }_i^c\left(W_p^{*},\dot{\epsilon }\right)\text{=}{\sigma }_{iy}^c\left(1+b_i^c{(W_p^{*})}^{n_i^c}\right)\left(1+c_i^c\ln \left(\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)\right)$$

   Where, $i$ =1 or 2.

   In shear:(8)

   $${\sigma }_{12}^{}\left(W_p^{*},\dot{\epsilon }\right)\text{=}{\sigma }_{12y}^{}\left(1+b_{12}^{}{(W_p^{*})}^{n_{12}^{}}\right)\left(1+c_{12}^{}\ln \left(\frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}\right)\right)$$

   The superscripts $c$ and $t$ represent compression and tension, respectively.

   Plastic work $W_p^{*}$ in above limiting stress is defined as:(9)

   $$W_p^{*}=\frac{W_p}{W_p^{ref}}$$

   Where, $W_p^{ref}$ is unit reference plastic work per volume.

   This criterion represents a second order closed three-dimensional Tsai-Wu surface in ${\sigma }_1$ , ${\sigma }_2$ and ${\sigma }_{12}$ 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 $d_i$

     Global tensile strain damage between ${\epsilon }_{ti}$ and ${\epsilon }_{fi}$ controlled by the damage factor $d_i$ , which is given by:

     $d_i=\min \left(\frac{{\epsilon }_i-{\epsilon }_{ti}}{{\epsilon }_i}\cdot \frac{{\epsilon }_{mi}}{{\epsilon }_{mi}-{\epsilon }_{ti}},d_{\max }\right)$ in directions, i = 1, 2

   • E-modulus
     E-modulus is reduced according to damage parameter if, ${\epsilon }_{ti}\le {\epsilon }_i\le {\epsilon }_{fi}$ :(10)

     $$E_{ii}^{reduced}=E_{ii}(1-d_i)$$
     E-modulus is reduced according to damage paramter, if ${\epsilon }_i>{\epsilon }_{fi}$ :(11)

     $$E_{ii}^{reduced}=E_{ii}(1-d_{\max })$$

     In this case, damage is set to $d_{\max }$ and it is not updated further.

   • Yield Stress
     Yield stress is reduced since below damage strain in different loading:

     • ${\epsilon }_i^{\text{t1}}$ and ${\epsilon }_i^{t2}$ in tension
     • ${\epsilon }_i^{\text{c1}}$ and ${\epsilon }_i^{c2}$ in compression
     • ${\epsilon }_{12}^{\text{1}}$ and ${\epsilon }_{12}^2$ in shear
     For example, tensile in direction 1 will be reduced when ${\sigma }_{1\max }^t$ at ${\epsilon }_i^{\text{t1}}$ and until residual stress ${\sigma }_{1rs}^t$ at ${\epsilon }_1^{t2}$ .

     
     
     Figure 1. Tensile in Direction 1

   • Element deletion is controlled by the I_off flag.

   Out-of-plane damage (delamination) with $\gamma$ .

   The simpliest delamination criterion is based on the evaluation of out-of-plane shear strains ( ${\gamma }_{31}$ and ${\gamma }_{23}$ ) with $\gamma =\sqrt{{({\gamma }_{13})}^2+{({\gamma }_{23})}^2}$ .

   • Element stresses and are gradually reduced if, ${\gamma }_{\max }>\gamma >{\gamma }_{ini}$
   • The element is completely removed (fails), if $\frac{\gamma -{\gamma }_{ini}}{{\gamma }_{\max }-{\gamma }_{ini}}>d_{3\max }$ 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 $W_p^{\max }$ or directional maximum plastic work $W_{ijp}^{\max }$ 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 ( ${\sigma }_{rs}>{\sigma }_y$ ), then the element layer ruptures (stress set to zero) if it reaches the directional maximum plastic work $W_{ijp}^{\max }$ . Example, tensile loading in direction 1 with ${\sigma }_{1rs}^t>{\sigma }_{1y}^t$ , element layer ruptured if plastic work reach ${{\displaystyle {\text{W}}_{\text{1}p}^{\max }}}^t$ .

     
     
     Figure 2.

     If the residual stress is not greater than yield stress ( ${\sigma }_{rs}\le {\sigma }_y$ ), then the element layer ruptures if it reaches the global maximum plastic work $W_p^{\max }$ . Example, tensile loading in direction 2 with ${\sigma }_{2rs}^t\le {\sigma }_{2y}^t$ , element layer ruptured if plastic work reach $W_p^{\max }$ .

     
     
     Figure 3.

     If WP_fail=1

     The element layer ruptures when it reaches the directional maximum plastic work in its direction $W_{ijp}^{\max }$ even if the residual stress is less than the yield stress.

   • Element deletion is controlled by the option I_off which uses the following criteria or combinations of criteria.
     • Element rupture could be due to reaching the strain criterion ( ${\epsilon }_i>\begin{array}{c}{\epsilon }_{\mathrm{m}i}\end{array}$ in direction $i$ )
     • Damage criterion ( $d_i>\begin{array}{c}{d}_{\max }\end{array}$ in direction $i$ )
     • 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 ICC_global=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)

       $$W_p^{\max }\cdot \left(1+c\ln \frac{{\dot{\epsilon }}_2}{{\dot{\epsilon }}_0}\right)$$
       and(13)

       $$W_{2p}^{{\max }^t}\cdot \left(1+c_2^t\ln \frac{{\dot{\epsilon }}_2}{{\dot{\epsilon }}_0}\right)$$
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 $W_p^{ref}$ is energy per unit of volume. If set $W_p^{ref}$ 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 $W_p^{ref}=1\left[\frac{J}{m^3}\right]$
   • If unit system of Ton-mm-s used in model, then $W_p^{ref}=1\left[\frac{mJ}{m{m}^3}\right]$
   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 $W_p^{ref}$ will be automatically converted. Leaving the $W_p^{ref}$ 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.