A Thermo-Magneto-Mechanically Coupled Constitutive Model of Magnetic Shape Memory Alloys

A macroscopic phenomenological constitutive model considering the martensite transformation and its reverse is constructed in this work to describe the thermo-magneto-mechanically coupled deformation of polycrystalline magnetic shape memory alloys (MSMAs) by referring to the existing experimental results. The proposed model is established in the framework of thermodynamics by introducing internal state variables. The driving force of martensite transformation, the internal heat production and the thermodynamic constraints on constitutive equations are obtained by Clausius dissipative inequality and constructed Gibbs free energy. The spatiotemporal evolution equation of temperature is deduced from the first law of thermodynamics. The demagnetization effect occurring in the process of magnetization is also addressed. The proposed model is verified by comparing the predictions with the corresponding experiments. It is concluded that the thermo-magneto-mechanically coupled deformation of MSMAs including the magnetostrictive and magnetocaloric effects at various temperatures can be reasonably described by the proposed model, and the magnetocaloric effect can be significantly improved over a wide range of temperature by introducing an additional applied stress.