Nonlinear magneto-mechanical finite element analysis of Ni–Mn–Ga single crystals

Abstract

This paper presents a three-dimensional (3D) nonlinear quasi-static isothermalfinite element formulation for single crystals of Ni–Mn–Ga ferromagnetic shapememory alloy (FSMA). This formulation is directly coupled (strong coupling)between the magnetic vector potential and mechanical displacement. As a result thisformulation is applicable to general structural configurations, where the mechanical andmagnetic behaviour of the entire structural and magnetic system can be computedsimultaneously. This finite element formulation has the potential for applications thatrequire accurate prediction of the magnetic field distribution and strain response ofNi–Mn–Ga single crystals. One of the major advantages of this finite elementformulation is the ability to predict the behaviour of the material for generalized orcomplicated shapes and geometries where analytical methods may not be adequate.The two-dimensional nonlinear finite element analysis computer software MAGSTRAN(magnetic structural analysis) is developed based on this formulation. Numerical results forselected examples are validated against experimental data available in the literature. It isdemonstrated that there is reasonable correlation between MAGSTRAN results andexperimental data available in the literature.