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[1] S. Conti, M. Lenz, and M. Rumpf. Hysteresis in magnetic shape memory composites: Modeling and simulation. J. Mech. Phys. Solids, 89:272-286, 2016.
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Magnetic shape memory alloys are characterized by the coupling between the reorientation of structural variants and the rearrangement of magnetic domains. This permits to control the shape change via an external magnetic field, at least in single crystals. Composite materials with single-crystalline particles embedded in a softer matrix have been proposed as a way to overcome the blocking of the reorientation at grain boundaries. We investigate hysteresis phenomena for small NiMnGa single crystals embedded in a polymer matrix for slowly varying magnetic fields. The evolution of the microstructure is studied within the rate-independent variational framework proposed by Mielke and Theil (1999). The underlying variational model incorporates linearized elasticity, micromagnetism, stray field and a dissipation term proportional to the volume swept by the twin boundary. The time discretization is based on an incremental minimization of the sum of energy and dissipation. A backtracking approach is employed to approximately ensure the global minimality condition. We illustrate and discuss the influence of the particle geometry (volume fraction, shape, arrangement) and the polymer elastic parameters on the observed hysteresis and compare with recent experimental results.