Interaction integral approach for the Evaluation of Crack-front Singularities in a Solid Cantilever Beam under Magneto-Electro-Elastic loading using XFEM

Abstract

In the piezoelectric energy harvesting devices, the most preferred is the cantilever beam orientation that can produce maximum deflection. Therefore, in this paper, three-dimensional fracture analysis of a cracked magneto-electro-elastic cantilever beam is studied using extended finite element methods (XFEM). The crack-front singularities like stress intensity factors (SIFs), electric displacement intensity factor (EDIF), and magnetic induction intensity factor (MIIF) are evaluated using the MEE interaction integral approach. The contour J-integral in domain form is solved with the asymptotic crack front fields as auxiliary fields using the Stroh formalism. The numerical results showed good agreement with the benchmark problem. Few case studies for the crack front singularities are presented using the proposed method. The results provided give useful guidance in the designing and manufacturing of smart devices.