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### PROP_DAMAGE_CL_ANISOTROPIC

###### Material properties
*PROP_DAMAGE_CL_ANISOTROPIC
"Optional title"
did, erode, noic, $\alpha_{irr}$, $\beta_{irr}$
$W_{0}$, $W_{90}$, $W_{t}$

#### Parameter definition

VariableDescription
did Unique damage identification number
erode Element erosion flag
options:
0 $\rightarrow$ failed element is not eroded
1 $\rightarrow$ failed element is eroded
2 $\rightarrow$ node splitting at failure (crack plane orthogonal to max principal strain)
3 $\rightarrow$ node splitting at failure (crack plane orthogonal max principal stress)
noic Flag to turn off cracking along interface between different materials
options:
0 $\rightarrow$ material interface cracks are allowed
1 $\rightarrow$ material interface cracks are not allowed
$\alpha_{irr}$ Irregularization factor
default: no irregularization
$\beta_{irr}$ Irregularization cap
default: $\beta_{irr}=1$
$W_{0}$ Damage parameter for the rolling/extrusion direction
$W_{90}$ Damage parameter for the transverse direction
$W_{t}$ Damage parameter for the material thickness direction

#### Description

This is an anisotropic Cockcroft-Latham like failure criterion. The material will fail once the damage parameter, $D$, has evolved from 0 to 1.

$\displaystyle{ D = \displaystyle{\int_0^{\epsilon_{eff}^p}} \frac{\mathrm{max}(0,\sigma_1)}{W_c} \mathrm{d}\epsilon_{eff}^p}$

where $\sigma_1$ is the maximum principal stress. $W_c$ is a weighted ductility parameter and it depends on the loading direction:

$\displaystyle{ W_c = \sqrt{ W_0^2 \cos^2 \alpha_0 + W_{90}^2 \cos^2 \alpha_{90} + W_t^2 \cos^2 \alpha_t }}$

$\alpha_0$, $\alpha_{90}$ and $\alpha_t$ are the angles between the maximum principle stress and the material rolling/extrusion, transverse and thickness directions, respectively.

The initial material orientation is defined using either INITIAL_MATERIAL_DIRECTION, INITIAL_MATERIAL_DIRECTION_VECTOR or INITIAL_MATERIAL_DIRECTION_WRAP.

The optional irregularization parameters $(\alpha_{irr}, \beta_{irr})$ are used to amplify the damage growth in regions where the Finite Element mesh is too coarse to accurately resolve the local variations of the strain field. The purpose is to significantly reduce the mesh dependency. Note that this irregularization procedure currently only is implemented for 64-node cubic hexahedra. It has no effect on other element types. The amplified rate of damage growth $\dot D_{amp}$ is defined as:

$\dot D_{amp} = \displaystyle{ (1 + \mathrm{min} (\alpha_{irr} \cdot \frac{\|\mathbf{\varepsilon}_a - \mathbf{\varepsilon}_b \|} {\|\mathbf{\varepsilon}_a + \mathbf{\varepsilon}_b \|}, \beta_{irr})) \cdot \dot D}$

where $(\mathbf{\varepsilon}_a, \mathbf{\varepsilon}_b)$ are the average strain tensors at the eight element center IP's and eight corner IP's, respectively. Hence, $\|\mathbf{\varepsilon}_a - \mathbf{\varepsilon}_b \|$ is a measure of the curvature of the strain field (in parametric space).