Features

This anisotropic brittle model is based on cleavage of least dense atomic planes. Cleavage is possible in three modes.

Local damage

The local damage $\phi_{l}$ is given by, \begin{equation} \label{eq: local damage} \phi_{l} = \min_{\alpha} \phi^{\alpha}, \end{equation}

Micro damage

\begin{equation} \label{eq: micro damage} \phi^{\alpha} = \min \left(1,\frac{1}{\delta^{\alpha}}\right), \end{equation}

Cleavage modes and Projection tensors

Mode $1$

Mode $2$

Mode $3$

$\mathbf{P}^{\alpha}_{m=3} = \hat{t}^{\alpha} \otimes \hat{n}^{\alpha} $

Cleavage opening rate

\begin{equation} \label{eq: Cleavage opening rate} \dot{\delta^{\alpha}} = \sum_{m=1}^{3} \dot{s_{0}}\left(\frac{\tnsr S^{*} \cdot \tnsr P^{\alpha}_{m}}{T_{c_{0}}\phi_{nl}}\right)^{n} \end{equation}

Damage Velocity Gradient

Damage Deformation Gradient

Parameters in material configuration