Non-singular anti-plane fracture theory of two parallel cracks within non-local functionally graded piezoelectric materials

Abstract

In this paper, the electromechanical behavior of two parallel cracks in functionally graded piezoelectric materials (FGPMs) by using non-local theory is investigated under the electric permeable boundary conditions. To overcome the mathematical difficulty, a one-dimensional non-local kernel is used instead of a two-dimensional one for the fracture problem to obtain the stress and the electric displacement fields near the crack tips. The effects of the crack length, the distance between two parallel cracks, the functionally graded parameter and the lattice parameter of the FGPMs on the stress and the electric displacement fields at the crack tips are discussed. The present solution exhibit no stress and electric displacement singularities at the crack tips. The non-local solutions yield a finite hoop stress and electric displacement at the crack tips.

Keywords

Solid mechanics two parallel cracks non-local theory FGPMs lattice parameter electromechanical behavior

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