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

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Elham Kiyani , M. Manav , Nikhil Kadivar , Laura De Lorenzis , George Em Karniadakis ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2501.00016

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.

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Nucleation Brittleness Operator (biology) Trunk Computer science Materials science Geology Composite material Physics Chemistry Biology Thermodynamics Ecology Biochemistry Repressor Transcription factor Gene

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2501.00016
PDF: https://arxiv.org/pdf/2501.00016
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Related Works: 10
OpenAlex ID: https://openalex.org/W4406051733

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DOI: https://doi.org/10.48550/arxiv.2501.00016

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

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Language: en

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Publication year: 2024

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Publication date: 2024-12-15

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Authors: Elham Kiyani, M. Manav, Nikhil Kadivar, Laura De Lorenzis, George Em Karniadakis

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Landing page: https://arxiv.org/abs/2501.00016

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Concepts: Nucleation, Brittleness, Operator (biology), Trunk, Computer science, Materials science, Geology, Composite material, Physics, Chemistry, Biology, Thermodynamics, Ecology, Biochemistry, Repressor, Transcription factor, Gene

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