Extending the Lattice Boltzmann Method to non-linear elastodynamics

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. • Extends Lattice Boltzmann Method (LBM) to non-linear solid mechanics. • Uses a moment-chain approach with a constitutive forcing term. • Validated through uniaxial tension, shear, and bending wave tests. • Achieves second-order accuracy in bulk, first-order at boundaries. • Demonstrates potential for large deformations and dynamic simulations.