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Modelling transient stresses in dynamically loaded elastic solids using the Lattice Boltzmann Method

Faust, Erik ; Steinmetz, Felix ; Schlüter, Alexander ; Müller, Henning ; Müller, Ralf (2023)
Modelling transient stresses in dynamically loaded elastic solids using the Lattice Boltzmann Method.
In: PAMM - Proceedings in Applied Mathematics and Mechanics, 2023, 23 (1)
doi: 10.26083/tuprints-00024294
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Modelling transient stresses in dynamically loaded elastic solids using the Lattice Boltzmann Method
Language: English
Date: 7 August 2023
Place of Publication: Darmstadt
Year of primary publication: 2023
Publisher: Wiley‐VCH
Journal or Publication Title: PAMM - Proceedings in Applied Mathematics and Mechanics
Volume of the journal: 23
Issue Number: 1
Collation: 6 Seiten
DOI: 10.26083/tuprints-00024294
Corresponding Links:
Origin: Secondary publication DeepGreen

In solids subjected to transient loading, inertial effects and S‐ or P‐wave superposition can give rise to stresses which significantly exceed those predicted by quasi‐static models. It pays to accurately predict such stresses – and the failures induced by them – in fields from mining to automotive safety and biomechanics. This, however, requires costly simulations with fine spatial and temporal resolutions.

The Lattice Boltzmann Method (LBM) can be used as an explicit numerical solver for certain appropriately formulated conservation laws [1]. It encodes information about the field variables to be simulated in distribution functions, which are modified locally and propagated across a regular lattice. As the LBM lends itself to finely discretised simulations and is easy to parallelise [2, p.55], it is an intriguing candidate as a solver for dynamic continuum problems.

Recently, Murthy et al. [3] and Escande et al. [4] adopted LBM algorithms to model isotropic, linear elastic solids. We extended these algorithms using local boundary rules that allow us to model arbitrary‐valued Dirichlet and Neumann boundaries. Here, we illustrate applications of the LBM for solids and the proposed additions by way of a simple numerical example – a glass pane subject to a sudden impact load.

Identification Number: e202200163
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-242944
Additional Information:

Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)

Classification DDC: 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 13 Department of Civil and Environmental Engineering Sciences > Mechanics > Continuum Mechanics
Date Deposited: 07 Aug 2023 08:20
Last Modified: 17 Oct 2023 08:03
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/24294
PPN: 512222436
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