Coupled 2D electric, magnetic, and mechanical fields in dielectrics with cracks and thin inclusions

Abstract

We apply methods of the theory of thermoelastic deformation of bodies with thin inclusions to study magnetoelectroelastic media with thin inhomogeneities. We construct the integral equations of the problem and propose an efficient numerical procedure of the boundary-element method for their solution. It is established that the fields of mechanical stresses, electric displacements, and magnetic induction near the tip (front) of a thin inclusion, the mathematical model of which can be based on the coupling principle for continua of different dimensions, have a square-root singularity. For the complete description of asymptotic relations for stresses, displacements, and other quantities near the front of an inhomogeneity, we introduce 10 generalized intensity factors for stresses, electric displacements, and magnetic induction. We obtain analytical solutions of the problem for the limiting cases of a permeable crack and a rigid electroconductive inclusion in a magnetoelectroelastic medium. Results of the numerical analysis of intensity factors for an elastic isotropic inclusion in an anisotropic magnetoelectroelastic medium are presented.