/FAIL/LAD_DAMA

This failure model is available for orthotropic solids and thick shells. It could also be used with Plyxfem in shell property /PROP/TYPE17 as an interplay material failure model. This failure model is compatible with /MAT/LAW12 (3D_COMP), /MAT/LAW14 (COMPSO) and /MAT/LAW25 (COMPSH) and /MAT/LAW1 (ELAST) (only when used with Plyxfem).

Format

Definitions

Example (Composite)

#RADIOSS STARTER
/UNIT/1
unit for mat and failure
#              MUNIT               LUNIT               TUNIT
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/COMPSH/1/1
composite example
#              RHO_I
             .001506
#                E11                 E22                NU12     Iform                           E33
              144000               10000                 .25         0                         20000
#                G12                 G23                 G31              EPS_f1              EPS_f2
                4200                4200                4200                   0                   0
#             EPS_t1              EPS_m1              EPS_t2              EPS_m2                dmax
                   0                   0                   0                   0                   0
#              Wpmax               Wpref      Ioff                         ratio
             1000000                   0         0                             0
#                  b                   n                fmax
                   0                   0             1000000
#            sig_1yt             sig_2yt             sig_1yc             sig_2yc               alpha
               10100               10100               10100               10100                   0
#           sig_12yc            sig_12yt                c_12          Eps_rate_0       ICC
               10068               10068                   0                   0         0
#          GAMMA_ini           GAMMA_max               d3max
                   0                   0                   0
#  Fsmooth                Fcut
         0                   0
/FAIL/LAD_DAMA/1/1
#                 K1                  K2                  K3              Gamma1              Gamma2
                2000                2000                2000               1E-20               1E-20
#                 Y0                  YC                   K                   A             Tau_max
                  40                 160              100000                   1                 .01
# Ifail_sh  Ifail_so                                                                               
         1         3
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

1. The Ladeveze failure damage model for delamination:(1)
   $${\text{Y}}_{{\text{d}}_3}={\frac{\partial {\text{E}}_{\text{D}}}{\partial {\text{d}}_3}|}_{\sigma =\text{cst}}=\frac{1}{2}\frac{{\langle {\sigma }_{33}\rangle }^2}{{\text{K}}_3{\left(1-{\text{d}}_3\right)}^2}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{Mode}\hspace{0.17em}I$$
   (2)
   $${\text{Y}}_{{\text{d}}_2}={\frac{\partial {\text{E}}_{\text{D}}}{\partial {\text{d}}_2}|}_{\sigma =\text{cst}}=\frac{1}{2}\frac{{{\sigma }_{32}}^2}{{\text{K}}_2{\left(1-{\text{d}}_2\right)}^2}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{Mode}\hspace{0.17em}II$$
   (3)
   $${\text{Y}}_{{\text{d}}_1}={\frac{\partial {\text{E}}_{\text{D}}}{\partial {\text{d}}_1}|}_{\sigma =\text{cst}}=\frac{1}{2}\frac{{{\sigma }_{31}}^2}{{\text{K}}_1{\left(1-{\text{d}}_1\right)}^2}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\text{Mode}\hspace{0.17em}\mathrm{III}$$

   
   
   Figure 1.

   ²

   For Quad 2D element, only Mode II and Mode III are available.

   Where, $d_i$ is the internal damage parameters associated with its fracture mode.

   The damage evolution law is controlled by equivalent damage energy release rate.

   $Y=Y_{d_3}+{\gamma }_1{Y}_{d_1}+{\gamma }_2{Y}_{d_2}$ with $Y_{d_i}|{}_t=\sup Y_{d_i}|{}_{\tau \le t}$

   The evolution of the damage parameters is strongly coupled with coupling factor ${\gamma }_1$ and ${\gamma }_2$ . These two material parameters come from delamination tests.

   For the present failure model, consider that $d_1=d_2=d_3=d$ .

   Damage value d increases at certain velocity:(4)

   $$\dot{d}=\frac{k}{a}\left[1-\exp \left(-a\langle w\left(Y\right)-d\rangle \right)\right]$$

   if $d<1$ .

   Otherwise, $d=1$

   While,

   $a$ is a measure of the failure ductility, the lower the value the more ductile the failure.

   $\frac{a}{k}$ is the minimum failure duration. The duration of the energy between $Y_0$ and $Y_c$ should be at least equal to $\frac{a}{k}$ .(5)

   $$\langle x\rangle =\{\begin{array}{c}x\mathit{if}x>0\\ 0\mathit{if}x<0\end{array}$$
   The function $w(Y)$ is computed as:(6)

   $$w(Y)=\frac{\langle \sqrt{Y}-\sqrt{Y_0}\rangle }{\sqrt{Y_c}-\sqrt{Y_0}}$$

   If the damage parameter $d\le 1.0$ , the stresses ${\sigma }_{33}$ , ${\sigma }_{13}$ and ${\sigma }_{23}$ are decreased according to the following function:

   A relaxation technique is used by gradually decreasing the stress:(7)

   $$\sigma (t)=\mathrm{f}(t)\cdot {\sigma }_d(t_r)$$
   With,(8)

   $$\mathrm{f}(t)=\exp \left(-\frac{t-t_r}{{\tau }_{\max }}\right)$$
   Where,

   $t$

   Time

   $t_r$

   Start time of relaxation when the damage criteria is assumed

   ${\tau }_{\text{max}}$

   Time of dynamic relaxation

   ${\sigma }_d\left(t_r\right)$

   Stress at the beginning of damage

2. The fail_ID is used with /STATE/BRICK/FAIL and /INIBRI/FAIL. There is no default value. If the line is blank, no value will be output for failure model variables in the /INIBRI/FAIL (written in .sta file with /STATE/BRICK/FAIL option).
3. After the failure criterion is reached, the ${\tau }_{\max }$ value determines a period of time when the stress in the failed element is gradually reduced to zero. When the stress reaches 1% of stress value at the start of failure, the element is deleted. This is necessary to avoid instabilities coming from a sudden element deletion and a failure “chain reaction” in the neighboring elements. Even if the failure criterion is reached, the default value of ${\tau }_{\max }=1.0E30$ results in no element deletion. Therefore, it is recommended to define ${\tau }_{\max }$ 10 times larger than the simulation time step.