A three-dimensional phenomenological model for Magnetic Shape Memory Alloys

We present a three-dimensional thermodynamically-consistent phenomenological model fo the magneto-mechanical behavior of magnetic shape memory materials featuring a cubic-totetragonal martensitic transformation. Existence of energetic solutions for both the constitutive relation problem and the three-dimensional quasi-static evolution problem are proved. The proposed model reduces to some former one via parameter asymptotics by means of a rigorous Gamma-convergence argument.