/FAIL/CHANG

Format

Definition

Comments

1. This failure model is available for shell only.
2. Where direction one is the fiber direction. The failure criteria for fiber breakage is written as:
   Tensile fiber mode: ${\sigma }_{11}>0$

   • For shells:(1)
     $$e_f{}^2={\left(\frac{{\sigma }_{11}}{{\sigma }_1^t}\right)}^2+\beta {\left(\frac{{\sigma }_{12}}{{\overline{\sigma }}_{12}}\right)}^2$$
   • For solids:(2)
     $$e_f{}^2={\left(\frac{{\sigma }_{11}}{{\sigma }_1^t}\right)}^2+\beta {\left(\frac{{\sigma }_{12}}{{\overline{\sigma }}_{12}}\right)}^2+{\left(\frac{{\sigma }_{13}}{{\overline{\sigma }}_{12}}\right)}^2$$
   Compressive fiber mode: ${\sigma }_{11}<0$ (3)

   $${e_c}^2={\left(\frac{{\sigma }_{11}}{{\sigma }_1^c}\right)}^2$$
3. For matrix cracking, the failure criterion is:
   Tensile matrix mode: ${\sigma }_{22}>0$

   • For shells:(4)
     $$e_m{}^2={\left(\frac{{\sigma }_{22}}{{\sigma }_2^t}\right)}^2+{\left(\frac{{\sigma }_{12}}{{\overline{\sigma }}_{12}}\right)}^2$$
   • For solids:(5)
     $$e_{m1}{}^2={\left(\frac{{\sigma }_{22}}{{\sigma }_2^t}\right)}^2+{\left(\frac{{\sigma }_{12}}{{\overline{\sigma }}_{12}}\right)}^2$$
     (6)
     $$e_{m2}{}^2={\left(\frac{\sigma 33}{{\sigma }_2^t}\right)}^2+{\left(\frac{{\sigma }_{13}}{{\overline{\sigma }}_{12}}\right)}^2$$
   Compressive matrix mode: ${\sigma }_{22}<0$

   • For shells:(7)
     $${e_d}^2={\left(\frac{{\sigma }_{22}}{2{\overline{\sigma }}_{12}}\right)}^2+\left[{\left(\frac{{\sigma }_2^c}{2{\overline{\sigma }}_{12}}\right)}^2-1\right]\frac{{\sigma }_{22}}{{\sigma }_2^c}+{\left(\frac{{\sigma }_{12}}{{\overline{\sigma }}_{12}}\right)}^2$$
   • For solids:(8)
     $${e_{d1}}^2={\left(\frac{{\sigma }_{22}}{2{\overline{\sigma }}_{12}}\right)}^2+[{\left(\frac{{\sigma }_2^c}{2{\overline{\sigma }}_{12}}\right)}^2-1]\frac{{\sigma }_{22}}{{\sigma }_2^c}+{\left(\frac{{\sigma }_{12}}{{\overline{\sigma }}_{12}}\right)}^2$$
     (9)
     $${e_{d2}}^2={\left(\frac{\sigma 33}{2{\overline{\sigma }}_{12}}\right)}^2+[{\left(\frac{{\sigma }_2^c}{2{\overline{\sigma }}_{12}}\right)}^2-1]\frac{\sigma 33}{{\sigma }_2^c}+{\left(\frac{{\sigma }_{13}}{{\overline{\sigma }}_{12}}\right)}^2$$
4. If the damage parameter $e_f{}^2,e_c{}^2,e_m{}^2$ , or ${e_d}^2\ge 1.0$ the stresses are decreased by using an exponential function to avoid numerical instabilities. A relaxation technique is used by decreasing the stress gradually:(10)
   $$\sigma (t)=\mathrm{f}(t)\cdot {\sigma }_d(t_r)$$

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

   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

5. The damage value, D is $0\le D\le 1$ . The status for fracture is:
   • Free, if $0\le D<1$
   • Failure, if $D=1$

   with $D=Max\left(e_f{}^2,e_c{}^2,e_m{}^2,e_d{}^2\right)$ . This damage value shows with /ANIM/SHELL/DAMA.

6. The fail_ID is used with /STATE/SHELL/FAIL and /INISHE/FAIL for shell. There is no default value. If the line is blank, a value will not be output for failure model variables in the /INIBRI/FAIL (written in .sta file with /STATE/BRICK/FAIL for brick and with /STATE/SHELL/FAIL for shell).
7. 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.