Phenomenological modeling for magneto-mechanical couplings of martensitic variant reorientation in ferromagnetic shape memory alloys

The paper presents a 2D phenomenological model to characterize the magneto-mechanical coupled behavior and its temperature dependences for martensitic variant reorientation in ferromagnetic shape memory alloys. A set of state variables are chosen to describe different microscopic mechanisms, and the evolution rules for the state variables are determined by minimizing the thermodynamic potential. The modified Landau free energy function is employed to account for the hysteretic switching between martensitic variants. It is assumed that the local switching thresholds are distributed due to the non-uniform internal stress throughout the specimen. The governing equation for martensite reorientation is then homogenized by taking this distribution property into account. The concept of density reassignment is also deployed to improve the modeling accuracy for partial reorientations. To validate the model capability, the model formulation is numerically implemented for the typical loading condition (i.e., uniaxial stress and a perpendicular magnetic field). As one of the superiorities, the temperature-dependent properties are remarked for the proposed model as well. Comparisons between the model predictions and the experimental results demonstrate the model capability in addressing the magneto-mechanical couplings and the temperature dependences of martensite reorientation.