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. In a similar way, using results by Rindler we prove the existence of optimal controls for a suitably large class of cost functionals.
Lussardi, L., Eleuteri, M., Thermal control of a rate-independent model for permanent inelastic effects in shape memory materials, <<EVOLUTION EQUATIONS AND CONTROL THEORY>>, 2014; 3 (3): 411-427. [doi:10.3934/eect.2014.3.411] [http://hdl.handle.net/10807/59535]