Enriched Element-Free Galerkin Method for Fracture Analysis of Functionally Graded Piezoelectric Materials

Abstract

A new method using the enriched element-free Galerkin method (EEFGM) to model functionally graded piezoelectric materials (FGPMs) with cracks was presented. To improve the solution accuracy, extended terms were introduced into the approximation function of the conventional element-free Galerkin method (EFGM) to describe the displacement and electric fields near the crack. Compared with the conventional EFGM, the new approach requires smaller domain to describe the crack-tip singular field. Additionally, the domain of the nodes was not affected by the crack. Therefore, the visibility method and the diffraction method were no longer needed. The mechanical response of FGPM was discussed, when its material parameters changed exponentially in a certain direction. The modifiedJ-integrals for FGPM were deduced, whose results were compared with the results of the conventional EFGM and the analytical solution. Numerical example results illustrated that this method is feasible and precise.