Dirichlet and Neumann boundary conditions in a lattice Boltzmann method for elastodynamics

With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM) mimics second order Crank-Nicolson scheme for certain types of balance laws (Farag et al. [2021]). This allows explicit, highly parallelisable LBM to efficiently solve fundamental equations solid mechanics: conservation mass, linear momentum, and constitutive relations. To date, all algorithms simulation - see e.g. Murthy [2017], Escande [2020], Schl\"uter [2021] have been limited small strain case. Furthermore, typical interpretation in current (Eulerian) configuration is not easily extensible large strains, as topological changes complicate treatment boundary conditions. In this publication, we propose deformation geometrically constitutively nonlinear mechanics. facilitate versatile modelling, algorithm defined reference (Lagrangian) configuration.