Speaker
Description
The application of Lattice Boltzmann (LB) methods to solid mechanics has recently garnered significant interest. These methods promise exceptional performance in terms of computational complexity, exhibiting linear scaling behavior. Moreover, meshless approaches, such as LB schemes, demonstrate favorable properties when addressing large deformations or fractures.
Different schemes have been proposed with the Navier-Cauchy equation as the target equation, which are based on either wave decompositions [1,2] or the asymptotic expansion [3]. Another approach uses a moment-chain to replicate balance equations [4]. This relies on a constitutive forcing term [5] to model the material behavior of elastic solids. However, the existing LB schemes for solids have been restricted to linear elastic materials under small strains.
This presentation extends the moment-chain approach to accommodate non-linear materials with finite strains. By modifying the constitutive forcing term, we integrate general hyperelastic material models into the LB framework. Stress and strain measures are computed with regard to the reference configuration.
We validate the approach through numerical benchmarks, showcasing its performance across various material models. Furthermore, simulations of wave propagation illustrate the capability of the scheme in fully dynamical systems and demonstrate the method's potential for advancing computational techniques in non-linear elastodynamics.
[1] A. Schlüter, S. Yan, T. Reinirkens, C. Kuhn, and R. Müller, ‘Lattice Boltzmann Simulation of Plane Strain Problems’, PAMM (2021),
doi: 10.1002/pamm.202000119.
[2] A. Schlüter, H. Müller, and R. Müller, ‘Boundary Conditions in a Lattice Boltzmann Method For Plane Strain Problems’, PAMM (2021),
doi: 10.1002/pamm.202100085.
[3] O. Boolakee, M. Geier, and L. De Lorenzis, ‘A new lattice Boltzmann scheme for linear elastic solids: periodic problems’’, CMAME (2023),
doi: 10.1016/j.cma.2022.115756.
[4] E. Faust, A. Schlüter, H. Müller, F. Steinmetz, and R. Müller, ‘Dirichlet and Neumann boundary conditions in a lattice Boltzmann method for elastodynamics’, Comput Mech (2024), doi: 10.1007/s00466-023-02369-w.
[5] M. Escande, P. K. Kolluru, L. M. Cléon, and P. Sagaut, ‘Lattice Boltzmann Method for wave propagation in elastic solids with a regular lattice: Theoretical analysis and validation’, preprint at arXiv (2020),
doi: 10.48550/arXiv.2009.06404.
