A Closed Form Solution of a Crack in Magneto-Electro-Elastic Composites under Anti-Plane Shear Stress Loading

Abstract

In this paper, a closed form solution of a crack in magneto-electro-elastic composites under anti-plane shear stress loading is obtained for the permeable crack surface conditions. By using the Fourier transform technique, the problem can be solved with a pair of dual integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. In solving the dual integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. The closed form solutions of the stress intensity factor, the electric displacement intensity factor and the magnetic flux intensity factor are given. It can be obtained that the stress field is independent of the electric field and the magnetic flux.