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 . 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.