GLOBAL SOLUTION TO THE FULL ONE-DIMENSIONAL FREMOND MODEL FOR SHAPE-MEMORY ALLOYS

In this paper, we prove the existence and uniqueness of the solution t o the one-dimensional initial-boundary value problem resulting from th e Fremond thermomechanical model of structural phase transitions in sh ape memory materials. In this model, the free energy is assumed to dep end on temperature, macroscopic deformation and phase fractions. The r esulting equilibrium equations are the balance laws of (linear) moment um and energy, coupled with an evolution variational inequality for th e phase fractions. Fourth-order regularizing terms in the quasi statio nary momentum balance equation are not necessary, and, as far as we kn ow for the first time, all the non-linear terms of the energy balance equation are taken into account.