A full two-dimensional thermodynamic-based model for magnetic shape memory alloys

Magnetic shape memory alloys (MSMAs) are interesting materials because they exhibit considerable recoverable strain (up to 10%) and fast response time (higher than 1 kHz). MSMAs are comprised of martensitic variants with tetragonal unit cells and a magnetization vector that is innately aligned approximately to the short side of the unit cell. 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 presents a phenomenological thermodynamic-based model able to predict the response of an MSMA to any two-dimensional (2D) magneto-mechanical loading. The model presented here is more physical and less empirical than other models in the literature, requiring only three model parameters to be calibrated from experimental results. In addition, this model includes evolution rules for the magnetic domain volume fractions and the angle of rotation of the magnetization vectors based on thermodynamic requirements. The resulting model is calibrated using a single, relatively simple experiment. Model predictions are compared with experimental data from a wide variety of 2D magneto-mechanical load cases. Overall, model predictions correlate well with experimental results. Additionally, methods for calibrating demagnetization factors from empirical data are discussed, and results indicate that using calibrated demagnetization factors can improve model predictions compared with the same model using closed-form demagnetization factors.