Faust, Erik ; Schlüter, Alexander ; Müller, Henning ; Müller, Ralf (2022)
A Lattice Boltzmann Method for nonlinear solid mechanics in the reference configuration.
doi: 10.48550/arXiv.2208.13769
Report, Bibliographie
Kurzbeschreibung (Abstract)
With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM) mimics a second order Crank-Nicolson scheme for certain types of balance laws (Farag et al. [2021]). This allows the explicit, highly parallelisable LBM to efficiently solve the fundamental equations of solid mechanics: the conservation of mass, the balance of linear momentum, and constitutive relations. To date, all LBM algorithms for solid simulation - see e.g. Murthy et al. [2017], Escande et al. [2020], Schlüter et al. [2021] - have been limited to the small strain case. Furthermore, the typical interpretation of the LBM in the current (Eulerian) configuration is not easily extensible to large strains, as large topological changes complicate the treatment of boundary conditions. In this publication, we propose a large deformation Lattice Boltzmann Method for geometrically and constitutively nonlinear solid mechanics. To facilitate versatile boundary modelling, the algorithm is defined in the reference (Lagrangian) configuration.
| Typ des Eintrags: | Report |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Faust, Erik ; Schlüter, Alexander ; Müller, Henning ; Müller, Ralf |
| Art des Eintrags: | Bibliographie |
| Titel: | A Lattice Boltzmann Method for nonlinear solid mechanics in the reference configuration |
| Sprache: | Englisch |
| Publikationsjahr: | 22 August 2022 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | ArXiv.org |
| Kollation: | 13 Seiten |
| DOI: | 10.48550/arXiv.2208.13769 |
| URL / URN: | https://arxiv.org/abs/2208.13769 |
| Kurzbeschreibung (Abstract): | With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM) mimics a second order Crank-Nicolson scheme for certain types of balance laws (Farag et al. [2021]). This allows the explicit, highly parallelisable LBM to efficiently solve the fundamental equations of solid mechanics: the conservation of mass, the balance of linear momentum, and constitutive relations. To date, all LBM algorithms for solid simulation - see e.g. Murthy et al. [2017], Escande et al. [2020], Schlüter et al. [2021] - have been limited to the small strain case. Furthermore, the typical interpretation of the LBM in the current (Eulerian) configuration is not easily extensible to large strains, as large topological changes complicate the treatment of boundary conditions. In this publication, we propose a large deformation Lattice Boltzmann Method for geometrically and constitutively nonlinear solid mechanics. To facilitate versatile boundary modelling, the algorithm is defined in the reference (Lagrangian) configuration. |
| Freie Schlagworte: | Lattice Boltzmann Method, Nonlinear Solid Mechanics, Large Deformation, Reference Configuration, Transient Simulation |
| ID-Nummer: | arXiv:2208.13769 [cs.CE] |
| Zusätzliche Informationen: | Preprint |
| Fachbereich(e)/-gebiet(e): | 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Kontinuumsmechanik |
| Hinterlegungsdatum: | 12 Jul 2024 07:09 |
| Letzte Änderung: | 11 Okt 2024 10:29 |
| PPN: | 522182496 |
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