PROP_DAMAGE_CL_EXTENDED
FE
Material properties
"Optional title"
did, erode, noic
$W_c$, $\phi$, $\gamma$, $\sigma_s$, $t_s$, $\alpha_s$
Parameter definition
Description
This is the extended Cockcroft-Latham failure criterion. Damage is defined as:
$\displaystyle{D = \int_0^{\varepsilon_{eff}^p} \frac{\sigma_{eff}}{W_c} \mathrm{max}\left(0, \left(\phi\cdot \frac{\sigma_1}{\sigma_{eff}} + (1 - \phi)\cdot \frac{\left(\sigma_1 - \sigma_3\right)}{\sigma_{eff}}\right)^\gamma \right) \mathrm{d}\varepsilon_{eff}^p}$
$\varepsilon_{eff}^p$ is the effective plastic strain, $\sigma_{eff}$ is the effective stress and $\sigma_1$/$\sigma_3$ is the maximum/minimum principal stress.
The ductile failure criterion is complemented with an optional spall criterion. Spall fracture occurs when a spall damage parameter $D_s$ evolves from from 0 to 1.
$ \dot{D}_s = \left\{ \begin{array}{ccc} \frac{1}{t_s}\left(\frac{\sigma_1}{\sigma_s}-D_s\right) & : & \sigma_1 \leq \sigma_s \\ \frac{1}{t_s} \left(1 + \alpha_s \left(1 - \mathrm{e}^{-\frac{\sigma_1 - \sigma_s}{\alpha_s \sigma_s}} \right) - D_s\right) & : & \sigma_1 \gt \sigma_s \\ \end{array} \right. $
Note that the spall damage parameter $D_s$ is not necessarily monotonically growing. It grows if the first principal stress $\sigma_1$ is large and drops if $\sigma_1$ is small. The main purpose of this unconventional formulation is to filter numerical noise (such as stress oscillations from element erosion in contact interfaces).
