/FAIL/TENSSTRAIN

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Definition

Comments

1. The failure criteria is based on the damage calculation:(1)
   $$D=\frac{\epsilon -{\epsilon }_{t1}}{{\epsilon }_{t2}-{\epsilon }_{t1}}$$
   Where, $\epsilon$ is either the equivalent strain or maximum principal tensile strain depending on the S-Flag option. The stress is then reduced using the calculated damage value using this equation: (2)

   $$\sigma =\left(1-D\right)\sigma$$

   The damage, $D$ , can be plotted using /ANIM/Eltype/DAMA or /H3D/Eltype/DAMA. The progressive damage value is calculated based on the ratio of total strain and the final calculated total strain limit. The highest value is retained until the element reaches the failure limit. There is no accumulation and no load path dependency.

2. Equivalent strain is calculated using tensile strain equivalent of Rankine criterion:(3)
   $${\epsilon }_T=\frac{1}{3}{I}_1+\frac{2}{\sqrt{3}}\sqrt{J_2^d}\cos \theta$$
   Where,

   $I_1$

   First invariant of strain tensor.

   $J_2^d$

   Second invariant of strain deviator.

   For 2D (shells) this definition is reduced to:(4)

   $${\epsilon }_T=\frac{1}{\text{2}}\left({\epsilon }_{xx}+{\epsilon }_{yy}+\sqrt{{\left({\epsilon }_{xx}-{\epsilon }_{yy}\right)}^2+{\epsilon }_{xy}{}^2}\right)$$
3. When S-Flag=1, elements can be deleted when $D$ =1 for one integration point, the first pricinple strain ${\epsilon }_1>{\epsilon }_{f1}$ , or the second principal strain ${\epsilon }_2>{\epsilon }_{f2}$ is reached. Failure based on the principal tension strain for failure and element deletion, ${\epsilon }_{f1}$ or ${\epsilon }_{f2}$ , does not include damage and instead fails immediately.

   When S-Flag= 2 or 3, elements can be deleted when $D$ =1 for one integration point and ${\epsilon }_{f1}$ or ${\epsilon }_{f2}$ are not used.

4. When S-Flag= 2 or 3, it is possible to scale the defined total failure strain values, ( ${\epsilon }_{f1}$ or ${\epsilon }_{f2}$ ) based on element size or temperature using the following factors:(5)
   $$facto{r}_{el}=Fscal{e}_{el}\cdot {\mathrm{f}}_{el}\left(\frac{Siz{e}_{el}}{El\_ref}\right)$$
   Where,

   ${\mathrm{f}}_{el}$

   Element size correction factor function defined via fct_ID_el

   Size_el

   Characteristic element size

   (6)

   $$facto{r}_T=Fscal{e}_T\cdot {\mathrm{f}}_{{}_T}\left(T^{*}\right)$$
   Where, ${\mathrm{f}}_{{}_T}\left(T^{*}\right)$ is the function, $fct\_I{D}_T$ and Temperature $T^{*}$ is computed via:(7)

   $$T^{\ast }=\frac{T-T_{ini}}{T_{melt}-T_{ini}}$$

   It is recommended to use /HEAT/MAT to define the thermal parameters for material laws that support thermo-plasticity.

5. When S-Flag =3, the strain calculation is based on 1st principal strain value. For material numbers < 28 with shell elements, damage is not applied and failure is immediate.
6. 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 the .sta file with /STATE/BRICK/FAIL option).