A three-dimensional model of magneto-mechanical behaviors of martensite reorientation in ferromagnetic shape memory alloys

The large strain in Ferromagnetic Shape Memory Alloys (FSMA) is due to the martensite reorientation driven by mechanical stresses and/or magnetic fields. Although most experiments studying the martensite reorientation in FSMA are under 1D condition (uniaxial stress plus a perpendicular magnetic field), it has been shown that the 2D/3D configurations can improve the working stress and give much flexibility of the material's applications [He, Y.J., Chen, X., Moumni, Z., 2011. Two-dimensional analysis to improve the output stress in ferromagnetic shape memory alloys. Journal of Applied Physics 110, 063905]. To predict the material's behaviors in 3D loading conditions, a constitutive model is developed in this paper, based on the thermodynamics of irreversible processes with internal variables. All the martensite variants are considered in the model and the temperature effect is also taken into account. The model is able to describe all the behaviors of martensite reorientation in FSMA observed in the existing experiments: rotating/non-rotating magnetic-field-induced martensite reorientation, magnetic-field-assisted super-elasticity, super-elasticity under biaxial compressions and temperature-dependence of martensite reorientation. The model is further used to study the nonlinear bending behaviors of FSMA beams and provides some basic guidelines for designing the FSMA-based bending actuators.