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The lattice Boltzmann methods (LBM) are a group of numerical methods that are used to solve partial derivatives equations (PDE). These methods themselves relying on a discretization of the Boltzmann equation. When the PDE at stake are related to solid mechanics, the subset of LBM is called lattice Boltzmann methods for solids (LBMS).
The main categories of LBMS are: vectorial distributions, wave solvers, force tuning, etc.
The LBMS subset remains highly challenging from a computational aspect as much as from a theoretical point of view.
References
Frantziskonis, George N. (2011). "Lattice Boltzmann method for multimode wave propagation in viscoelastic media and in elastic solids". Physical Review E. 83 (6): 066703. doi:10.1103/PhysRevE.83.066703.