A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

Failure trajectories, probable failure zones, and damage indices are some of the key quantities of relevance in brittle fracture mechanics. High-fidelity numerical solvers that reliably estimate these relevant quantities exist but they are computationally demanding requiring a high resolution of the...

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Published in:Computer methods in applied mechanics and engineering Vol. 391; no. C; p. 114587
Main Authors: Goswami, Somdatta, Yin, Minglang, Yu, Yue, Karniadakis, George Em
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.03.2022
Elsevier BV
Elsevier
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ISSN:0045-7825, 1879-2138
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Abstract Failure trajectories, probable failure zones, and damage indices are some of the key quantities of relevance in brittle fracture mechanics. High-fidelity numerical solvers that reliably estimate these relevant quantities exist but they are computationally demanding requiring a high resolution of the crack. Moreover, independent simulations need to be carried out even for a small change in domain parameters and/or material properties. Therefore, fast and generalizable surrogate models are needed to alleviate the computational burden but the discontinuous and complex nature of fracture mechanics presents a major challenge to developing such models. We propose a physics-informed variational formulation of DeepONet (V-DeepONet) for brittle fracture analysis. V-DeepONet is trained to map the initial configuration of the defect to the relevant fields of interests (e.g., damage and displacements). Once the network is trained, the entire global solution can be rapidly obtained for any initial crack configuration and loading steps on that domain. While the original DeepONet is solely data-driven, we take a different path to train the V-DeepONet by imposing the governing equations in a variational form with some labeled data. We demonstrate the effectiveness of V-DeepOnet through two benchmarks of brittle fracture and verify its accuracy using results from high-fidelity solvers. Encoding the physical laws to the model with data enhancement in training renders the surrogate model capable of accurately performing both interpolation and extrapolation tasks. Considering that fracture modeling is very sensitive to fluctuations, the proposed V-DeepONet with a hybrid training strategy is able to predict the quantities of interests with good accuracy, which can be easily extended to a wide array of dynamical systems with complex responses.
AbstractList Failure trajectories, probable failure zones, and damage indices are some of the key quantities of relevance in brittle fracture mechanics. High-fidelity numerical solvers that reliably estimate these relevant quantities exist but they are computationally demanding requiring a high resolution of the crack. Moreover, independent simulations need to be carried out even for a small change in domain parameters and/or material properties. Therefore, fast and generalizable surrogate models are needed to alleviate the computational burden but the discontinuous and complex nature of fracture mechanics presents a major challenge to developing such models. We propose a physics-informed variational formulation of DeepONet (V-DeepONet) for brittle fracture analysis. V-DeepONet is trained to map the initial configuration of the defect to the relevant fields of interests (e.g., damage and displacements). Once the network is trained, the entire global solution can be rapidly obtained for any initial crack configuration and loading steps on that domain. While the original DeepONet is solely data-driven, we take a different path to train the V-DeepONet by imposing the governing equations in a variational form with some labeled data. We demonstrate the effectiveness of V-DeepOnet through two benchmarks of brittle fracture and verify its accuracy using results from high-fidelity solvers. Encoding the physical laws to the model with data enhancement in training renders the surrogate model capable of accurately performing both interpolation and extrapolation tasks. Considering that fracture modeling is very sensitive to fluctuations, the proposed V-DeepONet with a hybrid training strategy is able to predict the quantities of interests with good accuracy, which can be easily extended to a wide array of dynamical systems with complex responses.
ArticleNumber 114587
Author Karniadakis, George Em
Yu, Yue
Goswami, Somdatta
Yin, Minglang
Author_xml – sequence: 1
  givenname: Somdatta
  orcidid: 0000-0002-8255-9080
  surname: Goswami
  fullname: Goswami, Somdatta
  email: somdatta_goswami@brown.edu
  organization: Division of Applied Mathematics, Brown University, Providence, RI, United States of America
– sequence: 2
  givenname: Minglang
  orcidid: 0000-0001-7861-350X
  surname: Yin
  fullname: Yin, Minglang
  email: minglang_yin@brown.edu
  organization: Center for Biomedical Engineering, Brown University, Providence, RI, United States of America
– sequence: 3
  givenname: Yue
  surname: Yu
  fullname: Yu, Yue
  email: yuy214@lehigh.edu
  organization: Department of Mathematics, Lehigh University, Bethlehem, PA, United States of America
– sequence: 4
  givenname: George Em
  surname: Karniadakis
  fullname: Karniadakis, George Em
  email: george_karniadakis@brown.edu
  organization: Division of Applied Mathematics, Brown University, Providence, RI, United States of America
BackLink https://www.osti.gov/biblio/1842897$$D View this record in Osti.gov
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IngestDate Fri May 19 01:41:22 EDT 2023
Fri Jul 25 04:47:03 EDT 2025
Sat Nov 29 07:27:14 EST 2025
Tue Nov 18 20:49:35 EST 2025
Sun Apr 06 06:53:41 EDT 2025
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Issue C
Keywords Variational energy
Physics-informed learning
Phase-field
DeepONet
Surrogate modeling
Brittle fracture
Language English
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Snippet Failure trajectories, probable failure zones, and damage indices are some of the key quantities of relevance in brittle fracture mechanics. High-fidelity...
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SubjectTerms Accuracy
Brittle fracture
Brittle materials
Configurations
Damage
DeepONet
Domains
Fracture mechanics
Interpolation
Material properties
Materials failure
Phase-field
Physics-informed learning
Solvers
Surrogate modeling
Training
Variational energy
Title A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials
URI https://dx.doi.org/10.1016/j.cma.2022.114587
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https://www.osti.gov/biblio/1842897
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