Consistent incremental approximation of dissipation pseudo-potentials in the variational formulation of thermo-mechanical constitutive updates

In this paper, we detail a consistent approximate expression for incremental dissipation pseudo-potentials which appear in the variational formulation of coupled thermo-mechanical boundary-value problems. We explain why the most intuitive expression does not work in the case of an explicit temperature dependence in the dissipation, and propose an alternative expression ensuring consistent results when reducing the time increment towards zero.

► We discuss approximate expressions for incremental dissipation pseudo-potentials. ► The most intuitive expression does not work in general temperature-dependence cases. ► We propose an alternative expression ensuring consistent results. ► These results are illustrated on a simple thermo-visco-plasticity model.