Thermomechanical models for phase transitions and mechanical instability

The behaviour of materials involving solid/solid phase transitions may be modelled by more or less smooth laws which lead to convex or non convex bulk potentials. We consider a class of models which contains the Fremond model as the simplest one, and models obtained by introduction of interaction energies between the phases. A series of assumptions and developments as well as the introduction of the marginal function defined as the minimum of the specific energy give quasiconvexification and convexification of the Fremond modelling. By accepting local minima of the total energy as possible equilibrium state, we can find numerically hysteretic behaviours and fronts of phase transition. Different stochastic perturbations are introduced to improve the formulation, and the influence of the latent heat on the hysteretic loop is analysed.