Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases

Abstract

This paper presents an analytical method to investigate the magnetoelectric coupling effect that is a new product property of piezoelectric–piezomagnetic intelligent composites since it is not present in each constituent. Based on the eigenstrain formulation and the Mori–Tanaka theory, the magneto–electro–elastic Eshelby tensors and the effective material properties of the composite are obtained explicitly. Particularly when both the matrix and the inclusions of the composite are transversely isotropic with different magneto–electro–elastic moduli, and shapes of inclusions are of elliptical cylinder, circular cylinder, disk, and ribbon, simple and closed-form solutions for the magnetoelectric coupling coefficients are acquired. The solutions are a function of the shape of inclusion, phase properties, and volume fraction of inclusions. Moreover, the derived simple expressions also show that the magnetoelectric coupling coefficients vanish as the volume fraction of inclusions tends to zero or one. This verifies that the magnetoelectric coupling coefficients are absent in each phase of the composite.