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.

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.

Magnetic Shape Memory Alloys (MSMAs) are a type of smart material that exhibit a large amount of recoverable strain when subjected to an applied compressive stress in the presence of a magnetic field or an applied magnetic field in the presence of a compressive stress. These macroscopic recoverable strains are the result of the reorientation of tetragonal martensite variants. Potential applications for MSMAs include power harvesters, sensors, and actuators. For these applications, the stress is assumed to be applied only in the axial direction, and the magnetic field is assumed to be applied only in the transverse direction.To realize the full potential of MSMA and optimize designs, a mathematical model that can predict the material response under all potential loading conditions is needed. Keifer and Lagoudas [1, 2] developed a phenomenological model that characterizes the response of the MSMA to axial compressive stress and transversely applied magnetic field based on thermodynamic principles. In this paper, a similar thermodynamic framework is used. However, a simpler hardening function is proposed based on the observation that the reorientation phenomenon is the same in both forward and reverse loading, as well as under both magnetic and mechanical loading. The magnetic domains are redefined to more accurately reflect the magnetic field measured experimentally [3]. This revised model is shown to adequately predict the magneto-mechanical response of the MSMA in 2D loading, i.e. axial compressive stress and transversely applied magnetic field.