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3.6-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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3.6-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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Stress-Strain relationship according to Hooke's law. More...
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Stress-Strain relationship according to Hooke's law.
Hooke's law describes a linear stress-strain relationship.
\(\sigma=\mathbf{c}\epsilon\) with \(\epsilon=\frac{1}{2}( \; \mathrm{grad}( \mathbf{u})+\mathrm{grad}(\mathbf{u})^T)\)
Furthermore, homogeneous and isotropic materials are assumed.
As proportionality constants the first and second Lamé parameters are used.
The final stress-strain relationship yields the following:
\( \sigma= 2 \mu \epsilon+\lambda \mathrm{tr}(\epsilon)\mathbf{I} \)
1.9.3