A continuum thermodynamics model for the sensing effect in ferromagnetic shape memory Ni–Mn–Ga

A magnetomechanical model based on continuum thermodynamics is presented which describes the sensing effect in single-crystal ferromagnetic shape memory Ni–Mn–Ga. The model quantifies the stress and magnetization dependence on strain at different values of bias fields under isothermal conditions. A magnetic Gibbs energy is considered as the thermodynamic potential with Zeeman, magnetostatic, and anisotropy energy contributions. Constitutive equations for stress and magnetization are obtained in the isothermal case after restricting the process through the Clausius-Duhem inequality for the second law of thermodynamics. Mechanical dissipation and the microstructure of Ni–Mn–Ga are incorporated in the continuum model through the internal state variables volume fraction, domain fraction, and magnetization rotation angle. Closed-form solutions describing the evolution of the internal state variables are developed. The model requires only seven parameters identified from simple experiments: stress-strain curve at zero field, and easy-axis and hard-axis magnetization curves.