Crack Path Prediction with Operator Learning using Discrete Particle System data Generation

2025-05-15

arXiv.org

AI Summary

Accurate prediction of dynamic crack propagation is critical for failure analysis of engineering materials, particularly in complex scenarios involving crack–discontinuity interactions (e.g., with holes) that induce crack deflection or arrest. To address this, we propose a configuration-driven particle discretization (CPD) framework to generate high-fidelity crack evolution data on multi-geometry, non-conforming meshes. We further introduce Fusion DeepONet—the first application of Deep Operator Networks to fracture mechanics—establishing a spatiotemporal operator mapping from geometric parameters and time to crack trajectory. This approach overcomes conventional limitations of mesh dependency and continuity assumptions, employing a branch-trunk network architecture for cross-sample generalization. With only 32–45 training samples, it achieves high predictive accuracy; under non-fracturing conditions, its error is substantially lower than that of standard DeepONet. Results demonstrate superior efficacy and robustness for complex geometries and time-varying fracture problems.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Federated Web and WoT systems, including distributed, federated and edge-based data processing
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Accurately modeling crack propagation is critical for predicting failure in engineering materials and structures, where small cracks can rapidly evolve and cause catastrophic damage. The interaction of cracks with discontinuities, such as holes, significantly affects crack deflection and arrest. Recent developments in discrete particle systems with multibody interactions based on constitutive behavior have demonstrated the ability to capture crack nucleation and evolution without relying on continuum assumptions. In this work, we use data from Constitutively Informed Particle Dynamics (CPD) simulations to train operator learning models, specifically Deep Operator Networks (DeepONets), which learn mappings between function spaces instead of finite-dimensional vectors. We explore two DeepONet variants: vanilla and Fusion DeepONet, for predicting time-evolving crack propagation in specimens with varying geometries. Three representative cases are studied: (i) varying notch height without active fracture; and (ii) and (iii) combinations of notch height and hole radius where dynamic fracture occurs on irregular discrete meshes. The models are trained on 32 to 45 samples, using geometric inputs in the branch network and spatial-temporal coordinates in the trunk network. Results show that Fusion DeepONet consistently outperforms the vanilla variant, with more accurate predictions especially in non-fracturing cases. Fracture-driven scenarios involving displacement and crack evolution remain more challenging. These findings highlight the potential of Fusion DeepONet to generalize across complex, geometry-varying, and time-dependent crack propagation phenomena.

Problem

• Predicting crack propagation in materials with varying geometries
• Modeling crack interaction with discontinuities like holes
• Generalizing operator learning for time-dependent fracture phenomena

Innovation

• Using Constitutively Informed Particle Dynamics data
• Training DeepONet variants for crack prediction
• Combining geometric inputs with spatial-temporal coordinates