[Getdp] Obtain strain energy in linear elasticity
zoltan.csati at centralelille.fr
zoltan.csati at centralelille.fr
Mon Mar 9 18:11:50 CET 2020
Dear developers,
I would like to obtain a global quantity, the strain energy, defined as $U = 1/2 \int_\Omega \sigma:\varepsilon \mathrm{d}\Omega$, where $\Omega$ is the whole (2D) domain, $\sigma$ is the stress tensor and $\varepsilon$ is the strain tensor (the symmetric gradient of $u$). I modified the Lib_Elasticity_u.pro template file at two places
- the PostQuantity block within the PostProcessing module, by adding
{ Name energy; Value {
Integral { Type Global; [ 1/2. * SquNorm[{d ux}] ];
In Vol_Mec; Jacobian Vol; Integration Int; }
}
}
- the Operation block within the PostOperation module, by adding
Print[ energy, OnGlobal, File StrCat[resPath, "energy.txt"], Format SimpleTable ];
It gives a number, but of course 1/2. * SquNorm[{d ux}] is not the strain energy I want. Is there a simple way to define the $\varepsilon$ tensor and then take its contraction with the $\sigma$ tensor?
Thank you,
Zoltan Csati
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