Dynamic analysis of two collinear permeable Mode-I cracks in piezoelectric materials based on non-local piezoelectricity theory

Based on the non-local piezoelectricity theory, this paper is concerned with two collinear permeable Mode-I cracks in piezoelectric materials subjected to the harmonic stress wave. The paper aims to discuss this issue.

According to the Fourier transformation, the problem is formulated into two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces.

Finally, the dynamic non-local stress and the dynamic non-local electric displacement fields near the crack tips are obtained. Numerical results are provided to illustrate the effects of the distance between the two collinear cracks, the lattice parameter and the circular frequency of the incident waves on the entire dynamic fields near the crack tips, which play an important role in designing new structures in engineering.

Different from the classical solutions, the present solution exhibits no stress and electric displacement singularities at the crack tips in piezoelectric materials. It is found that the maximum stress and maximum electric displacement can be used as a fracture criterion.