Fracture mechanics with physics-informed AI

Phase-field modeling of fracture is a prominent fracture modeling approach which recasts the problem as a variational problem and promises to completely determine various complex fracture processes including crack nucleation, propagation, bifurcation, and coalescence, obviating the need for ad-hoc conditions. In this approach, a phase field is introduced which regularizes a crack. It is, however, a nonlocal model which introduces a small length scale. Resolving this length scale in computation is expensive. Hence, uncertainty quantification, design optimization, material parameter identification, among others, using this approach become prohibitively expensive. Deep learning offers a potential pathway to address this challenge. We explore the application of physics-informed neural networks (PINNs) and DeepONet (an operator learning framework) to phase-field fracture modeling with the aim to capture diverse fracture processes. The nonconvexity of the energy functional, and the initiation and evolution of the fields with sharp gradients governed by this energy are the two key challenges to learning the solution field. Guided by the challenges, we design a network, construct a loss function, and select an optimization scheme to learn the solution accurately. By solving some benchmark problems in the phase-field fracture literature, we exhibit the capability of the approaches to capture crack nucleation, propagation, kinking, branching and coalescence.

[1] Manav, M., Molinaro, R., Mishra, S., & De Lorenzis, L. (2024). Phase-field modeling of fracture with physics-informed deep learning. Computer Methods in Applied Mechanics and Engineering, 429, 117104.

[2] Kiyani, E., Manav, M., Kadivar, N., De Lorenzis, L., & Karniadakis, G. Predicting crack nucleation and propagation in brittle materials using deep operator networks with diverse trunk architectures. In preparation.

[3] Heinzmann, J., Carrara, P., Luo, C., Manav, M., Mishra, A., Nagaraja, S., Oudich, H., Vicentini, F., & De Lorenzis, L. (2024). Calibration and Validation of a Phase-Field Model of Brittle Fracture within the Damage Mechanics Challenge. Engineering Fracture Mechanics, 307, 110319.