A generalized 2D Bezier-based solution for stress analysis of notched epoxy resin plates reinforced with graphene nanoplatelets

In this study, a robust Bezier-based multi-step method is extended to accurately solve the governing fourth order complex partial differential equation (PDE) in linear elastic fracture mechanics (LEFM) problems. The Bezier technique was first introduced by the authors to solve initial value problems in one dimension. Now, the method is further extended to simultaneously solve Boundary Value Problems (BVPs) in orthogonal directions. To examine the accuracy and performance of the present method, the first-mode normalized stress intensity factor (SIF) of a 2D epoxy resin plate having an initial edge crack and reinforced with randomly oriented graphene nanoplatelets (GnP) is determined and compared with the associated exact analytical solution using the Bayesian statistical analysis. Besides, the impact of GnP aspect ratio on the normalized crack opening displacement (COD) of the reinforced matrix is elaborated for the first time in the literature. Results of the present study suggest that GnPs with maximum aspect ratio are most effective to enhance elastic properties of the plate and potentially limit the edge crack propagation. Specifically, inclusion of 0.5 and 1.0% of needle-shaped GnPs in a notched epoxy resin plate decrease the maximum normalized COD by 33 and 50%, respectively, while for square-shaped GnPs, these reductions are limited to 20 and 37%, respectively.

Automated summary

This study extends a robust Bezier-based method to solve the governing fourth order complex partial differential equation in linear elastic fracture mechanics problems and explores the impact of GnP aspect ratio on enhancing material properties. The results suggest that GnPs with maximum aspect ratio are most effective in improving elastic properties of the plate and potentially limiting crack propagation, providing valuable insights for material reinforcement.