A non isothermal Ginzburg-Landau model for phase transitions in shape memory alloys

A thermodynamical model for martensitic phase transitions in shape memory alloys is formulated in the framework of the Ginzburg-Landau approach to phase transitions. A single order parameter is chosen to represent the austenite parent phase and two mirror related martensite variants. A free energy previously proposed in the literature (Levitas et al. in Phys. Rev. B 66:134206, 2002; Phys. Rev. B 66:134207, 2002; Phys. Rev. B 68:134201, 2003) is employed, in its simplest form, as the main constitutive content of the model. In this paper we treat time-dependent Ginzburg-Landau equation as a balance law on the structure order and we couple it to a energy balance equation, thus allowing to account for the heat transfer processes. We obtain a coupled thermo-mechanical problem whose consistency with the Second Law is verified. Finally, a suggestion to expand the proposed model to a full three-dimensional description which accounts for the formation of different martensite variants is proposed.