Lattice Boltzmann methods for nonlinear solid mechanics

In our newest publication, Henning Müller presents a Lattice Boltzmann method for non-linear solid mechanics, building upon preliminary work by Erik Faust from RPTU Kaiserslautern-Landau.

This work constitutes a simple extension of a previous approach, using a moment-chain with a constitutive forcing term. The evaluation happens in the reference configuration, where the interaction force term is defined through typical stress-strain relations. The method is validated through benchmarks and simulations of wave propagation.

This publication shows the application of the LBM to solids with non-linear material laws for the first time, indicating the strong potential to solve dynamic systems with large deformations.

The article is available as open access in Computer Methods in Applied Mechanics and Engineering:

Müller, H., Faust, E., Schlüter, A., Müller, R. Extending the Lattice Boltzmann Method to non-linear elastodynamics, Comput. Methods Appl. Mech. Eng. 438, 118076 (2025). DOI: 10.1016/j.cma.2025.118076