Magnetic Shape Memory Alloys (MSMAs) are a category of active materials which can be excited by magnetic field. These alloys have been used in sensor and actuator applications recently. MSMAs possess special properties such as large magnetic field-induced strains (up to %10) and high actuation frequency (about 1kHz), while ordinary shape memory alloys can’t act in frequencies above 5Hz due to the time involved with heat transformation. In this paper, MSMAs are modeled by an incremental modeling approach which utilizes different secant moduli for different parts of stress-strain curve. Furthermore, stress-strain curve of MSMAs is approximated using an analytical expression. The incremental model is used in predicting magnetic-field-induced strain either under the influence of mechanical stress or in the absence of stress. In this study, magnetic field equivalent stress is considered to be dependent on the orientation of martensitic variants during variant reorientation while it has been supposed to be a constant value in the previous works. This way, calculation of the magnetic field equivalent stress is modified to predict the superelastic behavior of MSMAs under constant field as well as variable stress. Results obtained from the incremental model are compared with experimental observations as well as other theoretical results available in the literature. This comparison shows a good correlation between the results of the model and experimental observations.

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