THERMOMECHANICAL EVOLUTION OF SHAPE MEMORY ALLOYS

In certain alloys, after deformation the original shape can be recovered just by thermal means. This shape memory behaviour can be interpreted as the effect of an austenite-martensite phase transition. We model this phenomenon by assuming the free energy to depend on the volumetric proportions of the different phases. The thermo-mechanical evolutions of a three dimensional body of such a material is here modelled in the framework of a second gradient theory. A variational formulation in Sobolev spaces is given; existence and uniqueness of the solution are proven by means of a fixed point argument.