Fracture analysis of interfacial crack in piezoelectric bimaterial by XIGA approach using Bézier extraction of NURBS

Abstract

This work presents analyses of interfacial crack in piezoelectrics bimaterial plate under electromechanical loading environment by extended isogeometric analysis (XIGA) approach using Bézier extraction of NURBS. Asymptotic crack–tip branch functions and discontinuous Heaviside function are implemented for local enrichment in the approximation of isogeometric analysis for capturing singularity at cracktip and discontinuity across surfaces of a crack. Bézier extraction of NURBS–based basis functions are implemented in discretization of domain for approximating both unknown field solution and geometries. The Bézier extraction operation decomposes the NURBS basis functions into a set of linear combination of Bernstein polynomials and a set of C 0 –continuity Bézier elements. Domain–form interaction integral is implemented to obtain generalized fracture parameters. To assess the robustness and accuracy in results obtained from XIGA, numerical results are first validated from analytical ones and then additionally, few numerical problems are solved for calculating the fracture parameters in terms of normalized intensity factors with respect to shear loads, electrical loads, crack orientation angle and angle of polarization.