Physics-Informed Neural Networks (PINNs) is a numerical simulation method that combines neural networks with material constitutive models (PDEs).
PINNs can be used to solve fracture mechanics problems without the need for discretizing the mesh. When using PINNs to solve fracture mechanics problems, it is usually necessary to embed the physical equations and initial/boundary conditions as constraints into the neural network training process to ensure that the network’s predictions meet the requirements of the physical equations. By optimizing the loss function, the neural network can be trained to predict unknown variables in fracture mechanics problems, such as displacement fields and stress fields.
However, it is important to note that the handling of singular regions at the crack tip directly affects the accuracy of the final fracture mechanics parameters (such as stress intensity factors, energy release rates, etc.) when using numerical methods for fracture mechanics analysis. The paper incorporates asymptotic expressions that characterize the oscillatory nature of crack tip displacement and stress fields into the training of the neural network, allowing for predictions that satisfy physical constraints. The advantage of using PINNs to solve fracture mechanics problems is that it can improve prediction accuracy by learning the constraints of physical equations and initial/boundary conditions. Furthermore, compared to traditional methods, PINNs have less discretization error and grid dependency.