This paper presents an energy relaxation-based approach for the modeling of single crystalline magnetic shape memory alloy response under general two-dimensional magneto-mechanical loading. It relies on concepts of energy relaxation in the context of non-convex free energy landscapes whose wells define preferred states of straining and magnetization. The constrained theory of magnetoelasticity developed by DeSimone and James [1] forms the basis for the model development. The key features that characterize the extended approach are (i) dissipative effects, accounted for in an incremental variational setting, and (ii) finite magnetocrystalline anisotropy energy. In this manner, important additional response features, e.g. the hysteretic nature, the linear magnetization response in the pre-variant reorientation regime, and the stress dependence of the maximum field induced strain, can be captured, which are prohibited by the inherent assumptions of the constrained theory. The enhanced modeling capabilities of the extended approach are demonstrated by several representative response simulations and comparison to experimental results taken from literature. These examples particularly focus on the response of single crystals under cyclic magnetic field loading at constant stress, and cyclic mechanical loading at constant magnetic field.

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