A generic homogenization model for magnetoelectric multiferroics

Abstract

A generic homogenization modeling framework which incorporates crystallographic domain features is introduced and computationally implemented for magnetoelectric multiferroics of all symmetries. The homogenization, mathematically applicable to heterogeneous media with contrasts in physical properties, replaces the heterogeneity of the multiferroics by an equivalent effective medium with uniform physical characteristics. A statistically representative unit-cell is proposed to encompass all forms of multiferroics and their composites in bulk. The variational formulation of the coupled magneto-electromechanical problem reveals the nature of interaction between mechanical, electrical, and magnetic fields of a multiferroic at a microscopic scale with high resolution. Furthermore, the mathematical homogenization theory of the multiferroic is implemented in finite element method by solving the coupled equilibrium electrical, magnetic, and mechanical fields. A “multiferroic finite element” is conceived for this purpose. The model is applied to a two-phase multiferroic magnetoelectric composite to demonstrate its validity by characterizing the equivalent physical properties.