Extended isogeometric analysis for fracture in functionally graded magneto-electro-elastic material

Abstract

In this work, we present an extended isogeometric analysis (XIGA) for cracked functionally graded magneto-electro-elastic (FGMEE) material. The material properties inside the FGMEE domain vary exponentially. An electrically and magnetically impermeable crack in the FGMEE domain is modeled by adding appropriate enrichment functions into the isogeometric analysis (IGA) approximation. Heaviside function is utilized to model the displacement, electric, and magnetic potential along the crack face. In contrast, conventional four-field crack tip enrichment functions are used to mimic the crack tip singularity characteristics. The generalized intensity factors (IFs), i.e., the stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF), are assessed using magneto-electro-mechanical interaction integral. A series of numerical studies over the cracked homogeneous and FGMEE material are presented. The accuracy of XIGA is examined by comparing the obtained results with the reference solutions. Various parameters such as volume fraction, crack length, loading combination parameter (both electrical and magnetic), material non-homogeneity parameter and crack orientation are taken to examine their effects on the generalized IFs.