A Constitutive Model of Coupled Magneto-thermo-mechanical Hysteresis Behavior for Giant Magnetostrictive Materials

This paper presents a three-dimensional constitutive model for predicting nonlinear magnetostrictive strain and magnetization responses for giant magnetostrictive materials subject to a variety of mechanical stresses and magnetic fields at various thermal environments. It is formulated based on a microscopically based phenomenological approach by utilizing a Gibbs free energy following by a Taylor series expansion with respect to stress, magnetization and temperature fields. The macroscopic nonlinear elastic strain depended on the magnetized state of each magnetic domain is derived through a volume average over microscopic magnetostrictions of magnetic domains. A generalized Jiles-Atherton model is used to describe hysteresis mechanism based on domain wall motion. The constitutive behavior obtained using the current model are correlated with experimental results. Parametric studies demonstrate that the proposed model is able to comprehensively examine the effect of compressive stresses and temperature deviations on the overall coupled hysteresis behavior for a giant magnetostrictive material subject to a dynamic magnetic loading. The proposed model will be useful for evaluating the contributions of different external stimuli, particularity for coupled stimuli, in giant magnetostrictive materials on their macroscopic responses. The constitutive relations are necessary for design of active devices that often contains giant magnetostrictive materials.