A phenomenological model for the magneto-mechanical response of single-crystal Magnetic Shape Memory Alloys

We advance a three-dimensional phenomenological model for the magneto-mechanical behavior
of magnetic shape memory alloys. Moving from micromagnetic considerations, we propose a
thermodynamically consistent constitutive relation which is able to reproduce the magnetically-
induced martensitic transformation in single crystals. Existence results for the constitutive
relation problem as well as for the corresponding quasi-static evolution system are illustrated
and convergence of time- and space-time-discretizations are recorded. Eventually, we present
algorithmic considerations and we numerically test the model in order to assess its ability in
reproducing the typical response of magnetic shape memory alloys, as well as in recovering
standard shape-memory and pseudo-elastic behaviors when no magnetic eld is present.