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Add elastic energy and plastic work computation to Mohr-coulomb state...

Sacha Duverger requested to merge add/mc_energies into parallel_s3

These changes add tracking for the elastic energy and the plastic work to the Mohr-Coulomb constitutive law, both being computed incrementally.

Elastic energy E_{el} (denoted svars_7 in csv files)

First we compute the elastic strain increment: d\epsilon_{ij}^{el} = \dfrac{1}{E}\left( (1+\nu)d\sigma_{ij} -\nu d\sigma_{kk}\delta_{ij} \right)

@jduriez Could you confirm that this expression is correct ? I have a doubt about the second term (where d\sigma_{kk} is the trace of the stress increment tensor).

Then we increment the elastic energy (its initial value is 0): E_{el}(t+\Delta t) = E_{el}(t) + v^p\sigma_{ij}(t+\Delta t)d\epsilon_{ij}^{el}

Plastic work W_{pl} (denoted svars_8 in csv files)

We compute the plastic strain simply as: d\epsilon_{ij}^{pl} = d\epsilon_{ij} - d\epsilon_{ij}^{el}

And then increment the plastic work (its initial value is 0): W_{pl}(t+\Delta t) = W_{pl}(t) + v^p\sigma_{ij}(t+\Delta t)d\epsilon_{ij}^{pl}

Edited by Sacha Duverger

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