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

This paper presents an analytical method to investigate the magnetoelectric coupling e€ect 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 e€ective material properties of the composite are obtained explicitly. Particularly when both the matrix and the inclusions of the composite are transversely isotropic with di€erent 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 coecients 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 coecients vanish as the volume fraction of inclusions tends to zero or one. This veri®es that the magnetoelectric coupling coecients are absent in each phase of the composite