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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. • Dynamic non-local theory solution to a mode-I crack in piezoelectric materials is studied. • The limited permeable conditions are applied at the crack faces. • The dynamic non-local stress and electric displacement fields near the crack tips are obtained. [ABSTRACT FROM AUTHOR]

The dynamic stress intensity factors (DSIFs) of two 3D rectangular cracks in a transversely isotropic elastic material under an incident harmonic stress wave are investigated by generalized Almansi’s theorem and the Schmidt method in the present paper. Using 2D Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, three pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the geometric shape of the rectangular crack, the characteristics of the harmonic wave and the distance between two rectangular cracks on the DSIFs of the transversely isotropic elastic material. [ABSTRACT FROM AUTHOR]