A full 3D thermodynamic-based model for magnetic shape memory alloys

Magnetic shape memory alloys (MSMAs) are interesting materials because they exhibit large recoverable strain (up to 10%) and fast response time (higher than 1 kHz). MSMAs are composed of martensitic variants with tetragonal unit cells and a magnetization vector that is approximately aligned with the short side of the unit cell in the absence of an external applied magnetic field. These variants reorient either to align the magnetization vector with an applied magnetic field or to align the short side of the unit cell with an applied compressive stress. This reorientation leads to a mechanical strain and an overall change in the material's magnetization, allowing MSMAs to be used as actuators, sensors, and power harvesters. This paper builds upon the work of Kiefer and Lagoudas as well as improvements proposed by LaMaster et al. to present a thermodynamic-based continuum model able to predict the response of an MSMA to any three-dimensional (3D) magneto-mechanical loading. The 3D nature of the model requires that the three variants, associated with the three axes of an MSMA single crystal, should all be allowed to evolve. In addition, this model includes evolution rules for the three magnetic domain volume fractions and the rotation of the direction of the magnetization vectors in each variant based on thermodynamic requirements.