A variational approach towards the modeling of magnetic field-induced strains in magnetic shape memory alloys

In this paper, the magneto-mechanical responses of a magnetic shape memory alloy (MSMA) sample are modeled through the variational approach. Motivated by the experimental results, a constitutive form for the effective magnetization vector is proposed. A (pseudo-)total energy functional for the whole magneto-mechanical system is then formulated, which takes into account the energy dissipations during the variant transformation process. By calculating the variations of the total energy functional with respect to the independent variables, the governing equation system for this model is derived, which is composed of the mechanical equilibrium equations, the magnetic field equations and some evolution laws for the internal variables. Under some simplifications, this model is used to study the magneto-mechanical responses of a MSMA sample under different magnetic and mechanical loading patterns. It can be seen that the results obtained in the model can capture the characteristic features of the field–strain, field–magnetization and stress–strain curves measured in the experiments.