A variational formulation for thermomechanically coupled low cycle fatigue at finite strains

In this paper, a constitutive model suitable for the analysis of Low Cycle Thermo-Mechanical Fatigue in metals is elaborated. The model is based on finite strain elastoplasticity coupled to continuum damage theory. It is embedded into a thermodynamical framework allowing to consistently capture the interplay between mechanics and thermal effects. It is shown that the fully coupled constitutive model can be re-written into a variationally consistent manner such that all (state) variables follow jointly and naturally from minimizing an incrementally defined functional. By discretizing this time-continuous functional in time by means of implicit integration schemes a numerically efficient implementation is proposed. In order to predict the temperature increase caused by plastic deformations realistically, the pre-loading history of the considered specimen is accounted for by non-zero initial internal variables. A comparison of the results predicted by the novel constitutive model to those corresponding to experiments (Ultimet alloy) shows that the predictive capabilities of the final model are excellent.