Features

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


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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}


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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} $


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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}


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Damage Velocity Gradient

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

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