Dynamic non-local theory analysis of multiple cracks in a FGPM under anti-plane shear waves

This paper investigates the dynamic interaction of multiple cracks in a functionally graded piezoelectric material (FGPM) plane subject to an anti-plane shear stress wave. The non-local theory and Schmidt method are used. Employing the Fourier transform techniques, the problem is converted to dual integral equations, which the unknown variables are jumps of displacements across the crack surfaces. The present solution exhibits no stress and electric displacement singularities at the crack tips and the stress and electric displacement fields near the crack tips are obtained. The non-local elastic solutions yield a finite hoop stress and electric displacement at the crack tips. This research will give us ideas on material selection for evaluating strength and preventing material failure of FGPM with multiple cracks.