Interfacial dynamic impermeable cracks analysis in dissimilar piezoelectric materials under coupled electromechanical loading with the extended finite element method

Interfacial dynamic impermeable cracks analysis of dissimilar piezoelectric solids under coupled electromechanical impact loadings by the extended finite element method (X-FEM) is presented. The dynamic X-FEM approach recently developed by the authors is further extended to analyze transient responses of interfacial impermeable cracks in dissimilar piezoelectric structures. The mechanical displacements and electrical potential are approximated by appropriate enrichment functions that are not only for the crack-face and crack-tips, but also for the materials interfaces. In this work, we develop a new set of electro-mechanical enrichment functions for interfacial crack-tip in piezoelectric bimaterials, which is modified from the pure mechanical twelve-fold interfacial crack-tip enrichment functions used for mechanical problems. Unlike the pure mechanical set, the new modified enrichment functions contain the electric-mechanical factor, which is determined from the electro-mechanical fields of interfacial cracks in piezoelectric bimaterials. We also present asymptotic crack-tip fields in piezoelectric bimaterials based on the Stroh’s formalism, and then apply them in the evaluation of generalized dynamic intensity factors (GDIFs) via the interaction integrals. The accuracy of the proposed approach is validated by comparing the obtained GDIFs with the ones derived from boundary element method. Numerical dynamic results of interfacial cracks in piezoelectric bimaterials are investigated and some aspects of the influences of poling angles, interface inclination, impact loading, etc. on the GDIFs are analyzed. There are many important issues have found such as the accuracy of the GDIFs obtained by the present formulation is high; a pure electrical impact immediately induces non-zero GDIFs, while the elastic waves caused by the mechanical impact need some time to reach and excite the crack; the effect of polarization on the GDIFs is significant; the behaviors of the GDIFs are complicated and their peak values decrease with increasing poling angles; the interface inclination angle of cracks greatly alters the GDIFs; and the interfacial crack growth may be delayed either by the effects of polarization or the electrical impacts.