Dynamic analytical solution of a limited-permeable mode-I crack in piezoelectric materials based on the non-local theory

Abstract

This paper presents the dynamic non-local theory solution to a limited-permeable mode-I crack in piezoelectric materials (PMs) with the crack surfaces subjected to harmonic stress waves. The generalized Almansi’s theorem and the Schmidt method are used for this purpose. Based on the Fourier transform technique, this problem is formulated into coupled dual integral equations. The dynamic non-local stress and the dynamic non-local electric displacement fields at the crack tips are obtained by solving the derived dual integral equations. Numerical results are reported and discussed to illustrate the influences of the crack length, the lattice parameter, the characteristics of the harmonic wave and the electric permittivity of the air inside the crack on the dynamic non-local stress field and the dynamic non-local electric displacement field near the crack tips in PMs. As compared to the known electrically permeable crack mode, the proposed one exhibits more applicability.