Fracture analysis of piezoelectric materials using the scaled boundary finite element method

This paper presents a technique to analyze two-dimensional fracture problems of piezoelectric materials. The proposed technique is based on the so-called scaled boundary finite element method, which only requires discretization on the boundary of the problem domain. The results of displacement and electric potential, stress and electric displacement at any point in the domain are analytically obtained. The stress and electric displacement intensity factors KI, KII and KIV are evaluated directly from the scaled boundary finite element solutions of the singular stress and electric displacement fields. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required. Numerical examples are presented to verify the proposed technique with the analytical solutions and the results from the literature. The present results highlight the accuracy, simplicity and efficiency of the proposed technique.