Abstract： Upon magneto-mechanical loadings, magnetic shape memory alloys (MSMA), can exhibit significant magnetic field-induced strain as well as stress-induced change of magnetization. These features make MSMA an important smart material in the application of actuator and sensor, which calls for deep understanding of the constitutive behavior of MSMA. Based on thermodynamics and dissipation of energy, we developed a three-dimensional constitutive model of MSMA under magneto-mechanical loadings. The martensitic transformation and reorientation are considered simultaneously. The evolution of the crystallographic and magnetic microstructure is described by using internal state variables. As for the simulation of magnetic microstructure, the single-domain assumption is usually adopted in literature, implying that the magnetic structure has evolved into a single-domain when the reorientation process begins. The single-domain assumption is believed to be suitable for the loading stage of magnetic field, but no longer valid for the unloading process. In the present model, we use the dual-domain model to simulate the evolution of the domain structure under cyclic loading. An arcsine function is selected to describe the macro magneto-mechanical responses induced solely by the evolution of magnetic domain. The simulation given by a reduced two-dimensional version of the present model, where the parameters are determined in terms of the experimental data of Ni2MnGa in literature, shows that the constitutive model developed in this paper is able to capture the magnetic shape memory effect and the hysteresis effect of strain as well as the magnetization response. The results predicted by the present model agree very well with experimental data, especially when the magnetic field is relatively low. It is believed that the present constitutive model can give good simulation for the strain and magnetization responses when MSMA is subjected to complex loading paths, especially the cases with unloading where the reverse reorientation is generally accompanied by the evolution of magnetic domains.
2016, Vol. 37 
