A XFEM approach for the three-dimensional cracks in piezoelectric material using interaction integral

[Display omitted] •Three dimensional crack modelling in piezoelectric material using XFEM is proposed.•The proposed method is extended to different three dimensional arbitrary crack geometries like inclined penny shaped crack, lens shaped crack and elliptical crack.•The method is used to determine the mixed stress intensity factors (SIF’s) and the electric displacement intensity factors (EDIF).•The new six enrichment functions for piezoelectric material spanning both stress and electric displacement singularities near crack front are successfully implemented.•The effectiveness, robustness and accuracy of the proposed method is verified with convergence test both with the mesh density and the actual values of planar penny shaped for Mode I and Mode IV intensity factors. Piezoelectric materials are widely used in various engineering applications such as electromechanical actuators, vibrators, energy harvesters, sensors, transducers, and propeller blades. These materials are subjected to various types of cyclic loading and their crack growth analysis is quite useful as it predicts the material’s life. This work proposes an extended finite element method to examine the static three-dimensional cracks in the piezoelectric material. The modeling of a crack is done using crack front elements enriched with the new six folded enrichment functions. These functions have been derived from the analytical solution of semi-infinite crack in a piezoelectric domain and expanded using Laurent-like series. Domain-based interaction integral is obtained to extract the mixed-mode stress intensity factors. Further, the auxiliary mechanical and the electrical fields in the interaction integral are obtained based on Stroh formulation. The XFEM is employed to evaluate SIF and EDIF in a three-dimensional domain is implemented in MATLAB code. The XFEM formulation is validated with static planar penny shaped crack for Mode I SIF and Mode IV EDIF with the standard solutions available in the literature. The error in Mode I and Mode IV is 0.0476 and 0.1444 respectively. The XFEM prediction values matches well with the analytical predictions. Further, simulation of the other cracks like inclined penny shaped crack, lens-shaped crack, and elliptical crack have been carried out with an expectation of usefulness of present methodology to mechanical engineers and designers.