Franke, Marlon ; Klein, Dominik K. ; Weeger, Oliver ; Betsch, Peter (2023)
Advanced discretization techniques for hyperelastic physics-augmented neural networks.
In: Computer Methods in Applied Mechanics and Engineering, 416
doi: 10.1016/j.cma.2023.116333
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
In the present work, advanced spatial and temporal discretization techniques are tailored to hyperelastic physics-augmented neural networks, i.e., neural network based constitutive models which fulfill all relevant mechanical conditions of hyperelasticity by construction. The framework takes into account the structure of neural network-based constitutive models, in particular, that their derivatives are more complex compared to analytical models. The proposed framework allows for convenient mixed Hu–Washizu like finite element formulations applicable to nearly incompressible material behavior. The key feature of this work is a tailored energy–momentum scheme for time discretization, which allows for energy and momentum preserving dynamical simulations. Both the mixed formulation and the energy–momentum discretization are applied in finite element analysis. For this, a hyperelastic physics-augmented neural network model is calibrated to data generated with an analytical potential. In all finite element simulations, the proposed discretization techniques show excellent performance. All of this demonstrates that, from a formal point of view, neural networks are essentially mathematical functions. As such, they can be applied in numerical methods as straightforwardly as analytical constitutive models. Nevertheless, their special structure suggests to tailor advanced discretization methods, to arrive at compact mathematical formulations and convenient implementations.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2023 |
| Autor(en): | Franke, Marlon ; Klein, Dominik K. ; Weeger, Oliver ; Betsch, Peter |
| Art des Eintrags: | Bibliographie |
| Titel: | Advanced discretization techniques for hyperelastic physics-augmented neural networks |
| Sprache: | Englisch |
| Publikationsjahr: | 6 September 2023 |
| Verlag: | Elsevier |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Computer Methods in Applied Mechanics and Engineering |
| Jahrgang/Volume einer Zeitschrift: | 416 |
| DOI: | 10.1016/j.cma.2023.116333 |
| URL / URN: | https://www.sciencedirect.com/science/article/pii/S004578252... |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | In the present work, advanced spatial and temporal discretization techniques are tailored to hyperelastic physics-augmented neural networks, i.e., neural network based constitutive models which fulfill all relevant mechanical conditions of hyperelasticity by construction. The framework takes into account the structure of neural network-based constitutive models, in particular, that their derivatives are more complex compared to analytical models. The proposed framework allows for convenient mixed Hu–Washizu like finite element formulations applicable to nearly incompressible material behavior. The key feature of this work is a tailored energy–momentum scheme for time discretization, which allows for energy and momentum preserving dynamical simulations. Both the mixed formulation and the energy–momentum discretization are applied in finite element analysis. For this, a hyperelastic physics-augmented neural network model is calibrated to data generated with an analytical potential. In all finite element simulations, the proposed discretization techniques show excellent performance. All of this demonstrates that, from a formal point of view, neural networks are essentially mathematical functions. As such, they can be applied in numerical methods as straightforwardly as analytical constitutive models. Nevertheless, their special structure suggests to tailor advanced discretization methods, to arrive at compact mathematical formulations and convenient implementations. |
| Freie Schlagworte: | finite element analysis, dynamic simulations, energy momentum scheme, mixed methods, hyperelasticity, physics-augmented neural networks, Computer Science - Computational Engineering, Finance, and Science |
| Zusätzliche Informationen: | Artikel-ID: 116333 |
| Fachbereich(e)/-gebiet(e): | Studienbereiche 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet Cyber-Physische Simulation (CPS) Forschungsfelder Forschungsfelder > Information and Intelligence Forschungsfelder > Information and Intelligence > Künstliche Intelligenz Studienbereiche > Studienbereich Computational Engineering |
| Hinterlegungsdatum: | 07 Sep 2023 05:31 |
| Letzte Änderung: | 21 Mai 2024 06:57 |
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| Suche nach Titel in: | TUfind oder in Google |
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Advanced discretization techniques for hyperelastic physics-augmented neural networks. (deposited 30 Jun 2023 09:29)
- Advanced discretization techniques for hyperelastic physics-augmented neural networks. (deposited 07 Sep 2023 05:31) [Gegenwärtig angezeigt]
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