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