Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures

2024-12-15

AI Summary

To address the prohibitively high computational cost of phase-field fracture simulation in brittle materials—hindering efficient, full-process prediction of crack nucleation, propagation, and branching—this work proposes a deep neural operator surrogate model integrating physical priors with a novel network architecture. Methodologically, it introduces three key innovations: (i) a two-stage DeepONet backbone that decouples learning tasks; (ii) a physics-informed DeepONet explicitly enforcing the phase-field energy functional, drastically reducing data dependency; and (iii) a Kolmogorov–Arnold network replacing conventional MLPs to enhance functional approximation efficiency. Validated on single-edge-notched specimens and one-dimensional bars, the model achieves accuracy comparable to full-order phase-field solvers, with prediction errors highly localized near crack fronts. Computational time is reduced by one to two orders of magnitude, demonstrating exceptional efficiency while preserving strong physical consistency.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high computational cost. To address this challenge, in this paper, we employ a deep neural operator (DeepONet) consisting of a branch network and a trunk network to solve brittle fracture problems. We explore three distinct approaches that vary in their trunk network configurations. In the first approach, we demonstrate the effectiveness of a two-step DeepONet, which results in a simplification of the learning task. In the second approach, we employ a physics-informed DeepONet, whereby the mathematical expression of the energy is integrated into the trunk network's loss to enforce physical consistency. The integration of physics also results in a substantially smaller data size needed for training. In the third approach, we replace the neural network in the trunk with a Kolmogorov-Arnold Network and train it without the physics loss. Using these methods, we model crack nucleation in a one-dimensional homogeneous bar under prescribed end displacements, as well as crack propagation and branching in single edge-notched specimens with varying notch lengths subjected to tensile and shear loading. We show that the networks predict the solution fields accurately, and the error in the predicted fields is localized near the crack.

Problem

• Predict crack nucleation and propagation in brittle materials
• Reduce computational cost of phase-field fracture modeling
• Enhance accuracy with diverse deep neural operator architectures

Innovation

• DeepONet with two-step trunk simplifies learning
• Physics-informed DeepONet enforces energy consistency
• Kolmogorov-Arnold Network replaces trunk neural network