A thermodynamically consistent two-dimensional constitutive model for magnetic shape memory alloys

Magnetic shape memory alloys (MSMAs) are a new class of smart materials that exhibit characteristics of large recoverable strains and high frequency. These unique characteristics, make MSMAs interesting materials for applications such as actuators, sensors, and energy harvesters. This paper presents a two-dimensional phenomenological constitutive model for MSMAs, developed within the framework of irreversible continuum thermodynamics. To this end, a proper set of internal variables is introduced to reflect the microstructural consequences on the material macroscopic behavior. Moreover, a stress-dependent thermodynamic force threshold for variant reorientation is introduced which improves the model accuracy in multiaxial loadings. Preassumed kinetic equations for magnetic domain volume fractions, decoupled equations for magnetization unit vectors and appropriate presentation of the limit function for martensite variant reorientation lead to a simple formulation of the proposed constitutive model. To investigate the proposed model capability in predicting the behaviors of MSMAs, several numerical examples are solved and compared with available experimental data as well as constitutive models in the literature. Demonstrating good agreement with experimental data besides possessing computational advantages, the proposed constitutive model can be used for analysis of MSMA-based smart structures.