Constitutive modeling of Ni–Mn–Ga ferromagnetic shape memory alloys under biaxial compression

Ferromagnetic shape memory alloys are a type of shape memory alloys that exhibit inelastic strains when subjected to magnetic fields. So far, several constitutive models have been proposed to predict ferromagnetic shape memory alloys’ behaviors under the application of a magnetic field and a compressive stress. In this article, an available constitutive model in a continuum framework is used to investigate the behaviors of Ni–Mn–Ga under biaxial compressive stresses. Since the required model parameters in the original approach are not unique for all loading conditions, the model is modified so that a unique set of model parameters suffices to study different loading conditions. Loading history is also considered in an improved way, and two-dimensional phase diagram is generalized to three-dimensional phase diagram, called reorientation surface in this work, to directly enter the effects of loading history on reorientation start conditions. The orthogonality property of a surface and its gradient vector are used to obtain the general conditions which must be satisfied to ensure continuation of reorientations.