Utilizing physics‐augmented neural networks to predict the material behavior according to Yeoh's law
This article discusses physics‐augmented neural network approaches in the field of hyperelastic material modeling. Physical conditions such as objectivity, material symmetry, or a stress– and energy‐free reference configuration are considered in the construction of the neural networks. In addition,...
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| Published in | Proceedings in applied mathematics and mechanics Vol. 24; no. 4 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
01.12.2024
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| Online Access | Get full text |
| ISSN | 1617-7061 1617-7061 |
| DOI | 10.1002/pamm.202400213 |
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| Abstract | This article discusses physics‐augmented neural network approaches in the field of hyperelastic material modeling. Physical conditions such as objectivity, material symmetry, or a stress– and energy‐free reference configuration are considered in the construction of the neural networks. In addition, a new approach for stress normalization is proposed. The neural network is used to learn the behavior of Yeoh's constitutive model with sparse data. Finally, the trained networks are incorporated into a three‐dimensional finite element framework and compared with the classical material model in terms of accuracy. The paper demonstrates the ability of physics‐augmented neural networks to model hyperelastic materials using a small amount of data that could be generated by experiments. Compared to the classical constitutive laws of Yeoh's model, our trained material showed no material instabilities that could occur due to poorly chosen material parameters. |
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| AbstractList | This article discusses physics‐augmented neural network approaches in the field of hyperelastic material modeling. Physical conditions such as objectivity, material symmetry, or a stress– and energy‐free reference configuration are considered in the construction of the neural networks. In addition, a new approach for stress normalization is proposed. The neural network is used to learn the behavior of Yeoh's constitutive model with sparse data. Finally, the trained networks are incorporated into a three‐dimensional finite element framework and compared with the classical material model in terms of accuracy. The paper demonstrates the ability of physics‐augmented neural networks to model hyperelastic materials using a small amount of data that could be generated by experiments. Compared to the classical constitutive laws of Yeoh's model, our trained material showed no material instabilities that could occur due to poorly chosen material parameters. |
| Author | Maurer, Lukas Kalina, Karl Eisenträger, Sascha Juhre, Daniel |
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| References_xml | – volume: 499 year: 2023 article-title: Viscoelastic constitutive artificial neural networks (vCANNs) – A framework for data‐driven anisotropic nonlinear finite viscoelasticity publication-title: Journal of Computational Physics – volume: 179 year: 2023 article-title: Neural networks meet hyperelasticity: A guide to enforcing physics publication-title: Journal of the Mechanics and Physics of Solids – volume: 180 year: 2023 article-title: Thermodynamically consistent neural network plasticity modeling and discovery of evolution laws publication-title: Journal of the Mechanics and Physics of Solids – volume: 121 start-page: 143 issue: 2 year: 2015 end-page: 234 article-title: The exponentiated Hencky‐logarithmic strain energy: Part I: Constitutive issues and rank‐one convexity publication-title: Journal of Elasticity – volume: 159 year: 2022 article-title: Polyconvex anisotropic hyperelasticity with neural networks publication-title: Journal of the Mechanics and Physics of Solids – volume: 70 start-page: 146 year: 2017 end-page: 155 article-title: Input convex neural networks publication-title: Proceedings of Machine Learning Research – volume: 398 year: 2022 article-title: Data‐driven tissue mechanics with polyconvex neural ordinary differential equations publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 125 year: 2022 article-title: Polyconvex neural networks for hyperelastic constitutive models: A rectification approach publication-title: Mechanics Research Communications – volume: 66 start-page: 754 issue: 5 year: 1993 end-page: 771 article-title: Some forms of the strain energy function for rubber publication-title: Rubber Chemistry and Technology – volume: 84 start-page: 1151 issue: 17‐18 year: 2006 end-page: 1163 article-title: Sliding behaviour of simplified tire tread patterns investigated by means of FEM publication-title: Computers & Structures – volume: 36 start-page: 659 issue: 5 year: 2009 end-page: 666 article-title: The Yeoh model applied to the modeling of large deformation contact/impact problems publication-title: International Journal of Impact Engineering – volume: 407 year: 2023 article-title: Modular machine learning‐based elastoplasticity: generalization in the context of limited data publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 377 year: 2021 article-title: Sobolev training of thermodynamic‐informed neural networks for interpretable elasto‐plasticity models with level set hardening publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 4 year: 2023 article-title: Parametrized polyconvex hyperelasticity with physics‐augmented neural networks publication-title: Data‐Centric Engineering – volume: 403 year: 2023 article-title: A new family of constitutive artificial neural networks towards automated model discovery publication-title: Computer Methods in Applied Mechanics and Engineering – volume: 40 start-page: 2767 issue: 11 year: 2003 end-page: 2791 article-title: Polyconvexity of generalized polynomial‐type hyperelastic strain energy functions for near‐incompressibility publication-title: International Journal of Solids and Structures – year: 2014 – year: 2015 – year: 2024 article-title: Viscoelasticty with physics‐augmented neural networks: Model formulation and training methods without prescribed internal variables publication-title: Computational Mechanics – year: 2010 – ident: e_1_2_6_5_1 doi: 10.1016/j.jmps.2023.105363 – volume-title: Mechanics of solid polymers: theory and computational modeling year: 2015 ident: e_1_2_6_14_1 – ident: e_1_2_6_17_1 doi: 10.1017/dce.2023.21 – ident: e_1_2_6_2_1 doi: 10.1016/j.mechrescom.2022.103993 – ident: e_1_2_6_15_1 doi: 10.1007/978-3-7091-0174-2_4 – ident: e_1_2_6_18_1 doi: 10.1016/S0020-7683(03)00086-6 – ident: e_1_2_6_11_1 doi: 10.5254/1.3538343 – ident: e_1_2_6_8_1 doi: 10.1016/j.jmps.2023.105416 – ident: e_1_2_6_7_1 doi: 10.1016/j.cma.2023.115930 – ident: e_1_2_6_21_1 doi: 10.1016/j.ijimpeng.2008.09.008 – ident: e_1_2_6_3_1 doi: 10.1016/j.cma.2022.115248 – ident: e_1_2_6_16_1 doi: 10.1007/s10659-015-9524-7 – ident: e_1_2_6_20_1 doi: 10.1016/j.compstruc.2006.01.010 – ident: e_1_2_6_9_1 doi: 10.1016/j.jcp.2023.112704 – ident: e_1_2_6_10_1 doi: 10.1007/s00466-024-02477-1 – ident: e_1_2_6_13_1 doi: 10.1016/j.cma.2022.115731 – volume-title: Nonlinear finite elements for continua and structures year: 2014 ident: e_1_2_6_12_1 – volume: 70 start-page: 146 year: 2017 ident: e_1_2_6_19_1 article-title: Input convex neural networks publication-title: Proceedings of Machine Learning Research – ident: e_1_2_6_4_1 doi: 10.1016/j.jmps.2021.104703 – ident: e_1_2_6_6_1 doi: 10.1016/j.cma.2021.113695 |
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| Title | Utilizing physics‐augmented neural networks to predict the material behavior according to Yeoh's law |
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