We present a three-dimensional thermodynamically-consistent phenomenological model for the magneto-mechanical behavior of magnetic shape memory materials featuring a cubic-to- tetragonal martensitic transformation. Existence of energetic solutions for both the consti- tutive 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 Γ-convergence argument.
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