Doubly periodic arrays of cracks and thin inhomogeneities in an infinite magnetoelectroelastic medium

A two-dimensional boundary element method for the analysis of a magnetoelectroelastic medium containing doubly periodic sets of cracks or thin inclusions is developed in this paper. The integral equations and closed-form expressions for corresponding kernels are obtained. Based on the quasi-periodicity of extended displacement and stress function, the integral representations for average stress, strain, electric displacement, magnetic induction etc. are developed. The algorithm of effective properties determination is given. The numerical examples prove the efficiency and high accuracy of the proposed approach in determination of stress, electric displacement and magnetic induction intensity factors and effective properties of the material containing doubly periodic arrays of cracks or thin inclusions.