[Getdp] Obtain strain energy in linear elasticity

[zoltan.csati at centralelille.fr]

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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