🤖 AI Summary
This work addresses the challenge of generalizing phase-field fracture modeling across arbitrary geometries throughout the entire process—from crack initiation to propagation—by proposing a hybrid integrated finite element–neural network (IFENN) solver. The method uniquely combines DeepOKAN and convolutional neural networks (CNNs) to separately model the initiation and propagation stages, while incorporating artificial boundary conditions to enhance far-field prediction accuracy. Requiring only a single physics-informed training on a reference geometry and leveraging a Gaussian-point sampling strategy, the approach substantially reduces offline computational costs. Numerical experiments demonstrate that the model achieves high accuracy and strong generalization capabilities on both seen and unseen geometries, significantly lowering computational resource demands.
📝 Abstract
In this paper we demonstrate how the Integrated Finite Element Neural Network (IFENN) framework can effectively model the entire evolution of phase-field fracture, including the initiation and propagation stage, across generalizable geometries. IFENN is a hybrid scheme for coupled computational mechanics problems, tightly coupling a standard FEM solver (mechanical equilibrium) with a pre-trained neural network (coupled field). In this work, the phase-field diffusion equation is approximated with: i) a DeepONet architecture with Kolmogorov-Arnold networks in the trunk and branch (DeepOKAN) for the initiation stage, and ii) a Convolution Neural Network (CNN) for the propagation stage. Both networks are trained only once, on a benchmark geometry, using a purely physics-informed approach based on the maximum strain energy and the phase-field variable. The training process utilizes an extremely small number of training increments and only a limited number of Gauss points that are strategically sampled from the fracture process zone. These features enable a substantial decrease of the offline training cost. To address the extrapolation of the DeepOKAN predictions in regions away from the crack tip during the inference stage, we implement a set of artificial boundary conditions to enforce the near-zero values in the far-field predictions. We showcase the flexibility and numerical accuracy of the proposed methodology across both the training and unseen geometries.