Magnetic shape memory alloys: three-dimensional modeling and analysis

We present a three-dimensional phenomenological model for the magneto-mechanical behavior of magnetic shape memory materials such as Ni 2MnGa. Moving from micromagnetic considerations, we advance to some thermodynamically consistent constitutive relations describing the magnetically-induced cubic-to-tetragonal martensitic transformation in a single crystal. We present an existence analysis for both the constitutive relation problem and the three-dimensional quasi-static evolution problem. Finally, we discuss the reduction of this model to some simpler one by means of a rigorous Gamma-convergence analysis.