Investigation of non-local theory solution to a three-dimensional rectangular permeable crack in magneto-electro-elastic materials

This paper presents the non-local theory solution to a three-dimensional rectangular permeable crack in magneto-electro-elastic materials (MEEMs) using the generalized Almansi's theorem and the Schmidt method. The problems are formulated through Fourier transform as three pairs of dual integral equations, in which the unknown variables are the jumps of elastic displacement, electric potential and magnetic potential jumps across the crack surfaces. The displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials to solve the dual integral equations and the resulting equations are solved using the Schmidt method. Numerical examples are provided to show the effects of the geometric shape of rectangular crack and the lattice parameter on the stress, the electric displacement and the magnetic flux fields near the crack edges in magneto-electro-elastic materials. Unlike the classical solution, the present solutions exhibit no stress, electric displacement and magnetic flux singularities near the crack edges in magneto-electro-elastic materials.