Transient dynamic crack analysis in non-homogeneous functionally graded piezoelectric materials by the X-FEM

We study transient dynamic fracture behaviors of stationary cracked functionally graded piezoelectric materials (FGPMs) under impact loading by using the extended finite element method (X-FEM). The material properties are assumed to be varied exponentially along one direction. A dynamic X-FEM model associated with the stable implicit integration technique is developed to serve that purpose, while the contour interaction integral technique is employed to accurately evaluate the relevant dynamic fracture parameters of FGPMs. Extensive numerical examples with the electrically impermeable crack-face boundary condition are considered, and the dynamic intensity factors (DIFs) obtained by the X-FEM are investigated in details. The accuracy of the developed model is verified by comparing the calculated dynamic responses with the solutions derived form the meshless local Petrov–Galerkin (MLPG) method and the finite element method (FEM), which shows an excellent agreement. The effects of the impact loads, poling direction, material gradation, electric displacements, material gradient coefficients, etc. on the DIFs are investigated in details. We have found that the dynamic crack behaviors in the non-homogeneous FGPMs are much more complicated than those in the homogeneous materials.