Non‐local stress and electric displacement solution of a 3D semi‐permeable rectangular crack in infinite orthotropic piezoelectric materials

Abstract

The paper presents the non-local stress and electric displacement solution of a 3D semi-permeable rectangular crack in infinite orthotropic piezoelectric materials (OPMs). With the help of the generalized Almansi's theorem and 2D Fourier transform, the boundary problem is formulated by three pairs of dual integral equations, and the displacement jumps across the crack surfaces are defined. The Schmidt method is used to solve the dual integral equations. The non-local stress field (NSF) and the non-local electric displacement field (NEDF) along the crack edges are deduced. Numerical results are reported to explain the influence of the size of the rectangular crack, the lattice parameter and the electric permittivity of the air inside the crack on the NSF and the NEDF at the crack edges in OPMs in detail. The present non-local solutions exhibit no stress and electric displacement singularities along the crack edges, and may be benefit future works.