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### PROP_DAMAGE_JC

###### Material properties
*PROP_DAMAGE_JC
"Optional title"
did, erode, noic, $\alpha_{irr}$, $\beta_{irr}$
$d_1$, $d_2$, $d_3$, $d_4$, $d_5$, $\epsilon_0$, $T_0$, $T_m$
$\epsilon_{min}$

#### 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: $\beta_{irr}=1$
$d_1$, $d_2$, $d_3$, $d_4$, $d_5$ Damage parameters
$\epsilon_0$ Reference strain rate
default: 1
$T_0$, $T_m$ Reference and melting temperatures
$\epsilon_{min}$ Minimum failure strain
default: 0

#### Description

This is the Johnson-Cook failure criterion. The material will lose its shear strength pressure once the damage parameter, $D$, has evolved from 0 to 1. The damage growth rate is defined as:

$\displaystyle{\dot D = \frac{\dot\epsilon_{eff}^p}{\mathrm{max}(\epsilon_{min}, \epsilon_f)}}$

where:

$\displaystyle{ \epsilon_f = (d_1 + d_2 \cdot \mathrm{e}^{\frac{\vert d_3 \vert \, p}{\sigma_{eff}}}) \cdot (1 + d_4 \cdot \mathrm{ln}(\frac{\dot\epsilon_{eff}^p}{\epsilon_0})) \cdot (1 + d_5 \cdot (\frac{\mathrm{T}-\mathrm{T}_0}{\mathrm{T}_m - \mathrm{T}_0}))}$

and:

$p = -(\sigma_{xx} + \sigma_{yy} + \sigma_{zz})/3$

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).