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 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Amsterdam
Elsevier B.V
01.03.2022
Elsevier BV Elsevier |
| Subjects: | |
| ISSN: | 0045-7825, 1879-2138 |
| Online Access: | Get full text |
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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. |
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| 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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| 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 |
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