Work

Extending the Lattice Boltzmann Method to non-linear elastodynamics

Year: 2025

Type: article

Abstract: This work outlines a Lattice Boltzmann Method (LBM) for geometrically and constitutively non-linear solid mechanics to simulate large deformations under dynamic loading conditions. The method utilises the moment chain approach, where the non-linear constitutive law is incorporated via a forcing term. Stress and deformation measures are expressed in the reference configuration. Finite difference schemes are employed for gradient and divergence computations, and Neumann- and Dirichlet-type boundary conditions are introduced. Numerical studies are performed to assess the proposed method and illustrate its capabilities. Benchmark tests for weakly dynamic uniaxial tension and simple shear across a range of Poisson’s ratios demonstrate the feasibility of the scheme and serve as validation of the implementation. Furthermore, a dynamic test case involving the propagation of bending waves in a cantilever beam highlights the potential of the method to model complex dynamic phenomena.

Source: Computer Methods in Applied Mechanics and Engineering

DOI: 10.1016/j.cma.2025.118076

Authors: Henning Müller, Erik Faust, Alexander Schlüter, Ralf Müller

Institutions: Technische Universität Darmstadt, Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau

Language: English

Topic: Lattice Boltzmann Simulation Studies

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,830

Funder: Deutsche Forschungsgemeinschaft