hookeslaw.hh File Reference

Stress-Strain relationship according to Hooke's law. More...

#include <dumux/flux/hookeslaw_fwd.hh>
#include <dumux/flux/box/hookeslaw.hh>

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Description

Hooke's law describes a linear stress-strain relationship.

$\sigma =\mathbf{c}ϵ$ with $ϵ=\frac{1}{2}(\mathrm{grad}(\mathbf{u})+\mathrm{grad}(\mathbf{u}{)}^T)$

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:

$\sigma =2\mu ϵ+\lambda \mathrm{tr}(ϵ)\mathbf{I}$

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