Fibrous composites of piezoelectric and piezomagnetic phases: Generalized plane strain with transverse electromagnetic fields

• We solve the field distributions of multiferroic fibrous composites under generalized plane strain with transverse EM fields.
• This coupling problem can be reduced to an equivalent plane elasticity problem through an eigenstrain.
• Muskhelishvili’s work on elastic composites is extended to the coupled ME problem.

This work presents a theoretical framework for solving the field distributions of a piezoelectric–piezomagnetic fibrous composite subjected to generalized plane strain with transverse electromagnetic fields. The matrix is infinite containing arbitrarily distributed circular cylinders, which may have different sizes and material properties. By introducing an eigenstrain corresponding to the electro-magneto-elastic effect, this coupling problem can be reduced to an equivalent plane elasticity problem. The classic work of Muskhelishvili to obtain the elastic potential of a composite is generalized to the current multi-field multi-inclusion media. Several numerical examples are presented to demonstrate the effectiveness of the approach.