Analysis of cracked functionally graded piezoelectric material using XIGA

Abstract

In this paper, an extended isogeometric analysis (XIGA) is presented to model the crack in functionally graded piezoelectric materials (FGPMs). The material properties of functionally graded piezoelectric material (FGPM) vary in an exponential manner along the length of the domain. To model a crack in the FGPM, the isogeometric analysis (IGA) approximation is enriched with the Heaviside and crack tip enrichment functions. Conventional four-fold enrichment functions of isotropic materials are employed to capture the crack tip singularity. To determine the fracture parameters, the domain form of electromechanical interaction integral is used. The accuracy of the proposed XIGA approach is highlighted by validating the several cracked homogeneous and functionally graded piezoelectric material against the analytical/reference solution available in the literature. Several example problems of cracked FGPM domain are solved by XIGA. The influence of material non-homogeneity parameter, loading combination parameter and crack length are examined on the stress intensity factors (SIFs) and electrical displacement intensity factor (EDIF).