A macroscopic model for magnetic shape-memory single crystals

A rate-independent model for the quasi-static magneto-elastic evolution of a magnetic shape-memory single crystal is presented. In particular, the purely mechanical Souza–Auricchio model for shape-memory alloys is here combined with classical micro-magnetism by suitably associating magnetization and inelastic strain. By balancing the effect of conservative and dissipative actions, a nonlinear evolution PDE system of rate-independent type is obtained. We prove the existence of so-called energetic solutions to this system. Moreover, we discuss several limits for the model corresponding to parameter asymptotics by means of a rigorous Γ-convergence argument.