Effective nonlinear responses of three-phase magnetoelectric composites.

A computational method, dubbed simplified unit-cell micromechanics model, is generalized and applied to establish the effective nonlinear responses of three-phase magnetoelectric composites that are composed of two distinct magnetostrictive and piezoelectric phases embedded in elastic polymer matrices. The nature of nonlinear constitutive behavior of each constituent is expected to significantly influence the overall responses of the composites. To obtain the effective nonlinear responses, a mathematical linearization is first introduced to perform the constitutive linearization for the nonlinear materials, and the resulting constitutive equations are then unified and nested into the micromechanics model followed by iterations in order to minimize errors from the linearization process. For the purpose of comparison, we also reformulate the well-established Mori-Tanaka micromechanics model insofar as its mathematical structure is aligned with that of the simplified unit-cell model. Numerical results are first validated against limited experimental measurements available in literature. Parametric studies are then conducted in order to reveal the effect of phase constitutive laws, volume fractions, and geometries on the overall nonlinear responses of there-phase magnetoelectric composites. The contributions of this work complement those of earlier studies that prevalently devoted to two-phase magnetoelectric composites and linear magneto-electro-elastic coupled responses only.