This paper proposes a multilevel three-dimensional constitutive model based on a microscopically phenomenological approach from the domain rotation mechanism, which is a fully coupled self-consistent homogenization scheme considering the interactions between elastic-inelastic strain and hysteresis. Considering the interactions among magnetic domains, grains, polycrystalline complexes, and macroscopic phenomenology, we predict the nonlinear magnetostrictive response of Terfenol-D under different types of external force loads and magnetic excitations in various thermal environments involving multi-fields of coupled magnetic, elastic, thermal, and mechanical phenomena. The average values of the mechanical bulk strains for different magnetization states are obtained at the grain scale utilizing Boltzmann functions and a self-consistent homogenization scheme. A Taylor series expansion of the Gibbs function concerning the field variables and an adapted Jiles-Atherton model are used to construct the hysteresis coupled constitutive relations at the macroscopic scale. The results associated with the experiments show that the established model can reasonably predict the magnetostrictive response under different external mixed stimuli. It can provide theoretical guidance for the precise control of nonlinear vibrations and the optimal design of the rotating giant magnetostrictive transducers at both microscopic and macroscopic multiple scales.
Keywords: domain switching; magnetostrictive material; nonlinear response.