Crack propagation in functionally graded porous plates by enriched Petrov-Galerkin natural element method

Enriched meshfree methods have been effectively used to predict the stress intensity factors (SIFs) and crack trajectories for homogeneous structures, but their applications to heterogenous materials were rarely reported. In this context, an enriched Petrov-Galerkin natural element method (PG-NEM) is introduced to simulate and examine the crack growth in 2-D heterogeneous functionally graded (FG) porous plates. The global displacement is approximated using Laplace interpolation (L/I) functions and enriched by introducing the crack-tip singular displacement and stress fields. The mixed-mode SIFs of FG plates characterized by the spatially varying elastic modulus are computed by the modified interaction integral method, and the crack trajectories are predicted by the maximum principal stress (MPS) criterion and the equivalent mode-I SIF. The advantage of proposed method is verified by comparing with the unriched PG-NEM and ANSYS. It is found that the prediction accuracy in crack trajectory is remarkably improved such that the crack trajectory of present method coincides well with one of ANSYS. Moreover, the present enriched method successfully simulates the crack trajectories of FG plates with the porosity as well as the spatially varying elastic modulus, and it is found that the crack growth characteristics are remarkably influenced by these parameters.