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:
$\dot D = \frac{\dot\epsilon_{eff}^p}{\epsilon_f}$
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).
