Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials
In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible...
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MDPI AG
2019-07-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/9/13/2706 |
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| author | Maruti Kumar Mudunuru Nishant Panda Satish Karra Gowri Srinivasan Viet T. Chau Esteban Rougier Abigail Hunter Hari S. Viswanathan |
| author_facet | Maruti Kumar Mudunuru Nishant Panda Satish Karra Gowri Srinivasan Viet T. Chau Esteban Rougier Abigail Hunter Hari S. Viswanathan |
| author_sort | Maruti Kumar Mudunuru |
| collection | DOAJ |
| description | In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a <i>k</i>-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity fracture mechanics model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective moduli at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are <inline-formula> <math display="inline"> <semantics> <mrow> <mo>≈</mo> <mi mathvariant="script">O</mi> <mo>(</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> times faster compared to high-fidelity fracture simulations by HOSS. These aspects make the proposed surrogate model attractive for upscaling damage from micro-scale models to continuum models. We would like to emphasize that the surrogate models are not a replacement of physical understanding of fracture propagation. The proposed method in this paper is limited to tensile loading conditions at low-strain rates. This loading condition corresponds to a dominant fracture perpendicular to tensile direction. The proposed method is not applicable for in-plane shear, out-of-plane shear, and higher strain rate loading conditions. |
| first_indexed | 2024-12-21T15:41:53Z |
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| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-12-21T15:41:53Z |
| publishDate | 2019-07-01 |
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| spelling | doaj.art-92f11266559b43aab203c8d891db6c0e2022-12-21T18:58:28ZengMDPI AGApplied Sciences2076-34172019-07-01913270610.3390/app9132706app9132706Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle MaterialsMaruti Kumar Mudunuru0Nishant Panda1Satish Karra2Gowri Srinivasan3Viet T. Chau4Esteban Rougier5Abigail Hunter6Hari S. Viswanathan7Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USATheoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USAEarth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USAX-Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USAEarth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USAEarth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USAX-Computational Physics Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USAEarth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USAIn brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but are highly computationally intensive, making them infeasible to incorporate in upscaling and uncertainty quantification frameworks. The goal of this paper is to provide a fast heuristic to reasonably estimate quantities such as failure path and damage in the process of brittle failure. Towards this goal, we first present a method to predict failure paths under tensile loading conditions and low-strain rates. The method uses a <i>k</i>-nearest neighbors algorithm built on fracture process zone theory, and identifies the set of all possible pre-existing cracks that are likely to join early to form a large crack. The method then identifies zone of failure and failure paths using weighted graphs algorithms. We compare these failure paths to those computed with a high-fidelity fracture mechanics model called the Hybrid Optimization Software Simulation Suite (HOSS). A probabilistic evolution model for average damage in a system is also developed that is trained using 150 HOSS simulations and tested on 40 simulations. A non-parametric approach based on confidence intervals is used to determine the damage evolution over time along the dominant failure path. For upscaling, damage is the key QoI needed as an input by the continuum models. This needs to be informed accurately by the surrogate models for calculating effective moduli at continuum-scale. We show that for the proposed average damage evolution model, the prediction accuracy on the test data is more than 90%. In terms of the computational time, the proposed models are <inline-formula> <math display="inline"> <semantics> <mrow> <mo>≈</mo> <mi mathvariant="script">O</mi> <mo>(</mo> <msup> <mn>10</mn> <mn>6</mn> </msup> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> times faster compared to high-fidelity fracture simulations by HOSS. These aspects make the proposed surrogate model attractive for upscaling damage from micro-scale models to continuum models. We would like to emphasize that the surrogate models are not a replacement of physical understanding of fracture propagation. The proposed method in this paper is limited to tensile loading conditions at low-strain rates. This loading condition corresponds to a dominant fracture perpendicular to tensile direction. The proposed method is not applicable for in-plane shear, out-of-plane shear, and higher strain rate loading conditions.https://www.mdpi.com/2076-3417/9/13/2706fracturegraph theory<i>k</i>-nearest neighborsmachine learningfailure pathsdamage statisticsbrittle failurefracture process zone |
| spellingShingle | Maruti Kumar Mudunuru Nishant Panda Satish Karra Gowri Srinivasan Viet T. Chau Esteban Rougier Abigail Hunter Hari S. Viswanathan Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials Applied Sciences fracture graph theory <i>k</i>-nearest neighbors machine learning failure paths damage statistics brittle failure fracture process zone |
| title | Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials |
| title_full | Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials |
| title_fullStr | Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials |
| title_full_unstemmed | Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials |
| title_short | Surrogate Models for Estimating Failure in Brittle and Quasi-Brittle Materials |
| title_sort | surrogate models for estimating failure in brittle and quasi brittle materials |
| topic | fracture graph theory <i>k</i>-nearest neighbors machine learning failure paths damage statistics brittle failure fracture process zone |
| url | https://www.mdpi.com/2076-3417/9/13/2706 |
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