A phenomenological constitutive model for magnetic shape memory alloys
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A thermodynamics-based constitutive model is derived which predicts the nonlinear strain and magnetization response that magnetic shape memory alloys (MSMAs) exhibit when subjected to mechanical and magnetic loads. The model development is conducted on the basis of an extended thermo-magneto-mechanical framework. A novel free energy function for MSMAs is proposed, from which the constitutive equations are derived in a thermodynamically-consistent manner. The nonlinear and hysteretic nature of the macroscopic material behavior is captured through the evolution of internal state variables which are motivated by the crystallographic and magnetic microstructures of MSMAs. Model predictions are presented for different relevant loading cases and analyzed in detail. Finally, magnetostatic boundary value problems for MSMAs are considered and numerically solved using the finite element method. For these computations the developed constitutive model provides the nonlinear magnetic properties of the MSMA. The knowledge of the magnetic field distribution in the computational domain as a function of the applied field, which results from this magnetostatic analysis, is useful for the proper interpretation of experimental results as well as the design of experiments and applications.