Thermal control of a rate-independent model for permanent inelastic effects in shape memory materials

We address the thermal control of the quasi-static evolution of a polycrystalline shape memory alloy specimen. The thermomechanical evolution of the body is described by means of an extension of the phenomenological Souza-Auricchio model accounting also for permanent inelastic effects. By assuming to be able to control the temperature of the body in time we determine the corresponding quasi-static evolution in the energetic sense. Using results by Rindler, we prove the existence of optimal controls for a suitably large class of cost functionals.