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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-12-01
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| Series: | Advanced Modeling and Simulation in Engineering Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s40323-024-00279-x |
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| Summary: | 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. |
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| ISSN: | 2213-7467 |