Add elastic energy and plastic work computation to Mohr-coulomb state...
These changes add tracking for the elastic energy and the plastic work to the Mohr-Coulomb constitutive law, both being computed incrementally.
E_{el}
(denoted svars_7 in csv files)
Elastic energy 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}
W_{pl}
(denoted svars_8 in csv files)
Plastic work 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}