Extended finite element simulation of stationary dynamic cracks in piezoelectric solids under impact loading

This work presents a transient dynamic analysis of stationary cracks in two-dimensional, homogeneous and linear piezoelectric solids subjected to coupled electromechanical impact loads using the extended finite element method (X-FEM). To serve this purpose, a dynamic X-FEM computer code using quadrilateral elements in conjunction with the level set method to accurately describe the crack geometry is developed. The sixfold basis enrichment functions particularly suitable for cracks in piezoelectric materials are adopted to fully capture the singular fields at the crack-tips in piezoelectricity. The governing equations are transformed into a weak-form and the time-dependent system of discrete equations is then obtained, which is solved by the unconditionally implicit time integration method at each time-step. To accurately assess the relevant dynamic mechanical stress and electric displacement intensity factors precisely and efficiently, domain-form of the contour integration integral taking the inertial effect into account in conjunction with the asymptotic near crack-tip fields of piezoelectric materials is presented. Four numerical examples for stationary cracks in homogeneous piezoelectric solids with impermeable crack-face boundary condition under impact loads are considered, respectively. Validation of the present method is made by comparing the present results with reference solutions available in the literature, and very good agreements are obtained. The effects of different poling directions and combined electromechanical impact loads are analyzed in details.