Data-driven material modeling based on the Constitutive Relation Error
Abstract Prior to any numerical development, the paper objective is to answer first to a fundamental question: what is the mathematical form of the most general data-driven constitutive model for stable materials, taking maximum account of knowledge from physics and materials science? Here we restri...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-12-01
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| Series: | Advanced Modeling and Simulation in Engineering Sciences |
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| Online Access: | https://doi.org/10.1186/s40323-024-00279-x |
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| author | Pierre Ladevèze Ludovic Chamoin |
| author_facet | Pierre Ladevèze Ludovic Chamoin |
| author_sort | Pierre Ladevèze |
| collection | DOAJ |
| description | Abstract Prior to any numerical development, the paper objective is to answer first to a fundamental question: what is the mathematical form of the most general data-driven constitutive model for stable materials, taking maximum account of knowledge from physics and materials science? Here we restrict ourselves to elasto-(visco-)plastic materials under the small displacement assumption. The experimental data consists of full-field measurements from a family of tested mechanical structures. In this framework, a general data-driven approach is proposed to learn the constitutive model (in terms of thermodynamic potentials) from data. A key element that defines the proposed data-driven approach is a tool: the Constitutive Relation Error (CRE); the data-driven model is then the minimizer of the CRE. A notable aspect of this procedure is that it leads to quasi-explicit formulations of the optimal constitutive model. Eventually, a modified Constitutive Relation Error is introduced to take measurement noise into account. |
| format | Article |
| id | doaj-art-5a764b6ff9584e4fa4c66e63b2d06fad |
| institution | OA Journals |
| issn | 2213-7467 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advanced Modeling and Simulation in Engineering Sciences |
| spelling | doaj-art-5a764b6ff9584e4fa4c66e63b2d06fad2025-08-20T02:32:26ZengSpringerOpenAdvanced Modeling and Simulation in Engineering Sciences2213-74672024-12-0111112710.1186/s40323-024-00279-xData-driven material modeling based on the Constitutive Relation ErrorPierre Ladevèze0Ludovic Chamoin1CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS-Laboratoire de Mécanique Paris-Saclay, Université Paris-SaclayCentraleSupélec, ENS Paris-Saclay, CNRS, LMPS-Laboratoire de Mécanique Paris-Saclay, Université Paris-SaclayAbstract Prior to any numerical development, the paper objective is to answer first to a fundamental question: what is the mathematical form of the most general data-driven constitutive model for stable materials, taking maximum account of knowledge from physics and materials science? Here we restrict ourselves to elasto-(visco-)plastic materials under the small displacement assumption. The experimental data consists of full-field measurements from a family of tested mechanical structures. In this framework, a general data-driven approach is proposed to learn the constitutive model (in terms of thermodynamic potentials) from data. A key element that defines the proposed data-driven approach is a tool: the Constitutive Relation Error (CRE); the data-driven model is then the minimizer of the CRE. A notable aspect of this procedure is that it leads to quasi-explicit formulations of the optimal constitutive model. Eventually, a modified Constitutive Relation Error is introduced to take measurement noise into account.https://doi.org/10.1186/s40323-024-00279-xData-driven modelingMaterials scienceConstitutive Relation ErrorElasto-(visco-)plasticity |
| spellingShingle | Pierre Ladevèze Ludovic Chamoin Data-driven material modeling based on the Constitutive Relation Error Advanced Modeling and Simulation in Engineering Sciences Data-driven modeling Materials science Constitutive Relation Error Elasto-(visco-)plasticity |
| title | Data-driven material modeling based on the Constitutive Relation Error |
| title_full | Data-driven material modeling based on the Constitutive Relation Error |
| title_fullStr | Data-driven material modeling based on the Constitutive Relation Error |
| title_full_unstemmed | Data-driven material modeling based on the Constitutive Relation Error |
| title_short | Data-driven material modeling based on the Constitutive Relation Error |
| title_sort | data driven material modeling based on the constitutive relation error |
| topic | Data-driven modeling Materials science Constitutive Relation Error Elasto-(visco-)plasticity |
| url | https://doi.org/10.1186/s40323-024-00279-x |
| work_keys_str_mv | AT pierreladeveze datadrivenmaterialmodelingbasedontheconstitutiverelationerror AT ludovicchamoin datadrivenmaterialmodelingbasedontheconstitutiverelationerror |