Graph Neural Network Framework to Emulate Multiple Crack Propagation, Crack Coalescence, and Stress Evolution in Brittle Materials

Emulating complex problems of fracture mechanics requires the use of existing, or newly developed high-fidelity models. These models typically work by solving intricate systems where computational costs and time requirements scale up with problem complexity. A possible solution to circumvent these challenges involves reduced-order modeling techniques, such as Machine Learning (ML). A recently developed ML method for emulating large-scale complex physics while reducing computational costs is Graph Neural Networks (GNNs). GNNs work by integrating supervised ML along with graph theory. This work develops a GNN based framework to simulate fracture and stress evolution in brittle materials due to multiple microcracks’ interaction. The GNN framework is trained on the dataset generated by XFEM-based fracture simulator. The framework consists of four GNNs: the first prediction stage determines Mode-I and Mode-II stress intensity factors (which can be used to compute the stress evolution), the second prediction stage determines propagating microcracks, and the final stage propagates crack-tip positions for the selected microcracks to the next time-step. Our framework achieves good prediction accuracy compared to an XFEM-based fracture simulator. The trained GNN framework is capable of emulating crack propagation, coalescence and corresponding stress distribution for a wide range of initial microcrack configurations (from 5 to 19 microcracks) without any additional modifications. Lastly, the framework’s simulation time shows speed-ups 6x-25x faster compared to an XFEM-based simulator.