Three-dimensional constitutive equations for Ni–Mn–Ga single crystals

This paper presents a formulation of isothermal three-dimensional (3D) quasi-static magneto-mechanical constitutive equations and 3D magnetisation constitutive equations for tetragonal martensite Ni–Mn–Ga FSMA single crystals (c/a<1)(c/a<1) with both ends restrained from twin-boundary motion. The formulated 3D constitutive equations model the 3D quasi-static magnetic fields as well as the coupling between uniaxial strains and stresses, and shear strains and stresses. The constitutive equations are compared with experimental results available in the literature and are found to correlate well with the experimental results, including magnetic field reversals. Both sets of 3D constitutive equations require only macroscopic parameters that are readily obtainable from magnetisation and mechanical stress–strain curves.