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Lattice Boltzmann methods (LBMs) stem from the computation of fluid flows. They work on the mesoscale with a statistical formulation based in kinetic theory. These methods promise great gains in the computational performance with good scaling for large systems. In recent years, an effort has been undertaken to develop LBMs for the simulation of solid mechanics as well.

For solids, long-range interactions are crucial. These are incorporated through force terms, which accounts for an important part of the constitutive model. The latest advancement handles non-linear solids with typical macroscopic stress-strain-relations.

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