Dynamic non-local theory solution to a permeable mode-I crack in a piezoelectric medium

In the present paper, the non-local theory, the generalized Almansi's theorem and the Schmidt method are developed for the analysis of a permeable mode-I crack in a piezoelectric medium(PZT-4, P-7, PZT-5H) under the harmonic stress waves. The problem is formulated through Fourier transformation into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The dynamic non-local stress and the dynamic non-local electric displacement are obtained at the crack tips. Numerical examples are provided to show the effects of the crack length, the characteristics of the harmonic wave and the lattice parameter on the dynamic stress field and the dynamic electric displacement field near the crack tips in a piezoelectric medium. Different from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack tips in a piezoelectric medium.