Micromechanics-based constitutive modeling of magnetostrictive 1–3 and 0–3 composites

Abstract

This study presents micromechanics models for the analysis of magneto-thermo-mechanical coupled hysteresis responses for magnetostrictive composites, comprising of an elastic polymer reinforced by magnetostrictive continuous fibers and particles, respectively, subjected to a cyclic magnetic field loading under various circumstances. Constitutive relation for the magnetostrictive reinforcements that can describe nonlinear strain and magnetic flux density in a variety of thermal environments is employed, while the polymeric matrix is assumed to be a linear elastic material. A simplified unit-cell micromechanics model is developed for the magnetostrictive composites whose microstructures are idealized with periodically distributed arrays of cubic representative unit cells. To obtain the overall nonlinear responses of the magnetostrictive composites, linearized micromechanical relations are first used to provide trial solutions followed by iterative schemes in order to correct errors from linearizing the nonlinear responses. The micromechanical estimations are validated by experimental data available in literature. For comparison, the Mori-Tanaka micromechanics model is further reformulated for the magnetostrictive composites. The presented micromechanical formulations can reveal the effects of constituent volume fraction, applied prestress, temperature, the geometry of the magnetostrictive reinforcement, and the direction of applied magnetic field on the overall performance of the magnetostrictive composites under periodic magnetic field loadings.