Non-local theory solution for a 3D rectangular permeable crack in piezoelectric composite materials

In the present paper, the non-local theory solution for a 3D rectangular permeable crack in piezoelectric composite materials under a normal stress loading is investigated by means of the generalized Almansi’s theorem and the Schmidt method. The double Fourier transform are used to solve the mixed boundary value problem as three pairs of dual integral equations. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The stress field and the electric displacement field near the rectangular crack edges are obtained. Numerical results are provided to illustrate the effects of the geometric shape of rectangular crack and the lattice parameter on the stress field and the electric displacement field near the crack edges in piezoelectric composite materials. Different from the classical solutions, it is found that the present solutions exhibit no stress and electric displacement singularities near the crack edges in piezoelectric composite materials.