Our previous work on ferromagnetic shape memory Ni50Mn28.7Ga21.3 demonstrates reversible compressive strains of -4100 microstrain along the [001] direction under the application of a magnetic field also along the [001] direction with no external orthogonal restoring force. The reversibility of the strains is due to internal bias stresses oriented orthogonal to the field. These results show promise for the use of Ni-Mn-Ga as the core material in solenoid transducers. In this paper, the reversible strains are explained by considering pinning sites as the source of the internal bias stresses in the material. Following prior work by Kiefer and Lagoudas, a phenomenological model is constructed for the motion of twin variants in the presence of an orthogonal pair formed by a magnetic field and an internal bias stress. The model is formulated by considering the Zeeman, elastic, and pinning energies, from which an appropriate Gibbs energy function is constructed. Minimization of the Gibbs function then yields a constitutive model for the strain. The accuracy of this model is studied and its implementation as a hysteresis kernel in homogenization theories is discussed.
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