A memory variable approach to modeling the magneto-mechanical behavior of magnetic shape memory alloys

Magnetic shape memory alloys (MSMAs) have attracted interest because of their considerable recoverable strain (up to 10%) and fast response time (1 kilohertz or higher). MSMAs are comprised of martensitic variants that have tetragonal unit cells and a magnetization vector that is innately aligned with the short side of the unit cell. These variants rotate 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 [4,5] as well as improvements proposed by LaMaster et al. [1] to present a thermodynamic based model to predict the response of an MSMA to axial mechanical loading and transverse magnetic loading. This work is unique, however, in its use of a memory variable, which references the last stable configuration. This is similar to the approach used by Saint-Sulpice [2] in modeling SMA wires. The resulting model has zero driving force for reorientation of variants at the beginning of any load and again when the load is removed. Thus the model predicts what is seen physically, that the material is stable when no magneto-mechanical load is present. Furthermore, this model is more physical and less empirical than others in the literature, having only 2 material parameters associated with the stress-strain or stress-field response. 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 and predictions are compared with both the more established Keifer and Lagoudas model as well as experimental data. Results show decent correlation with experiments. The model can be further improved by calibrating the demagnetization factor to experimentally measured changes in magnetic field.