$\def\rcontract{{\scriptscriptstyle\circ\bullet}} \def\lcontract{{\scriptscriptstyle\bullet\circ}}$

## 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, $$\label{eq: local damage} \phi_{l} = \min_{\alpha} \phi^{\alpha},$$

### Micro damage

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

## Cleavage modes and Projection tensors

### Mode $1$

$\mathbf{P}^{\alpha}_{m=1} = \hat{n}^{\alpha} \otimes \hat{n}^{\alpha}$

### Mode $2$

$\mathbf{P}^{\alpha}_{m=2} = \hat{d}^{\alpha} \otimes \hat{n}^{\alpha}$

### Mode $3$

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

## Cleavage opening rate

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

$$\label{eq: Damage Velocity Gradient} \tnsr L_{d} = \sum_{\alpha=1}^{ncs} \dot{\delta^{\alpha}}\tnsr{P}^{\alpha}$$

Integrating $\dot{\tnsr F}_{d} = \tnsr L_{d} \tnsr F_{d}$, we obtain $$\label{eq: Damage Deformation Gradient} \tnsr F_{d} = (\tnsr I -\tnsr L_{d} \Delta t)^{-1}\tnsr F_{d_{0}}$$

## Parameters in material configuration

To set the above parameters use the following (case-insensitive) naming scheme in a material.config file:

Parameter Name
$\dot{s_{0}}$ sdot0
$n$ damageratesensitivity
$ncs$ ncleavage
$\delta_{0}$ criticaldisplacement
$t_{0}$ criticalload
Topic revision: r7 - 03 Mar 2016, PhilipEisenlohr

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