A three-dimensional constitutive model for magnetic shape memory alloys under magneto-mechanical loadings

Abstract

This paper presents a three-dimensional phenomenological constitutive model for magnetic shape memory alloys (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. 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 show the model capability in reproducing the main features of MSMAs, several numerical examples are solved and compared with available experimental data as well as available three-dimensional 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.