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Features

This isotropic brittle model is based on rupture criterion and uses elastic strain energy $W_{e}$ as the driving force.

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Formulation

The governing equation of damage evolution sans the non local diffusion term is, \begin{equation} \label{eq: damage evolution} \mu\dot\phi_{nl} = \phi_{l} - \phi_{nl}, \end{equation} where $\mu$ is damage mobility, $\phi_{l}$ is local damage while $\phi_{nl} $is it non local counterpart.

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Driving force

The driving force for damage in this model is the elastic strain energy, $W_{e}$, which is calculated as, \begin{equation} \label{eq: strainenergy} W_{e} = \tnsr E : \tnsr S^{*}, \end{equation} where $\tnsr E =\frac{1}{2}(\tnsr F^{T}_{e}\tnsr F_{e} - \tnsr I) $ is the Green-Lagrange strain and $\tnsr S^{*} = \tnsrfour C : \tnsr E$, is its work conjugate, second Piola-Kirchhoff stress.
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Local damage

The local damage $\phi_{l}$ is given by, \begin{equation} \label{eq: local damage} \phi_{l} = \frac{W_{cr}}{W_{e}}, \end{equation} where, $W_{cr}$ is the critical strain energy at which damage starts to nucleate.
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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
$ W_{cr}$ criticalstrainenergy

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References

[1]
H.Ulmer, M. Hofacker, & & C. Miehe
Phase Field Modeling of Brittle and Ductile Fracture
PAMM · Proc. Appl. Math. Mech. 13, 533 – 536 (2013)
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Topic revision: r3 - 07 Jan 2015, LuvSharma

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