Towards a Lattice Boltzmann Method for Solids -Application to Static Equilibrium of Isotropic Materials

This paper presents a novel method for simulating the behavior of solid objects with the Lattice Boltzmann Method (LBM). To introduce and validate our proposed framework, comparative studies are performed for computing the static equilibrium of isotropic materials. Reminding that the LBM has strong theoretical foundations in the Boltzmann equation; this latter is firstly adjusted to solid motions, through its Boltzmann-Vlasov special case. Indeed, the prior equation usually characterizes collisionless plasma and serves here, when combined with a suitable mean-field external force term, for setting a reliable solid framework. Secondly, a library is built and plugged on the top of the well-known Parallel Lattice Boltzmann Solver (PaLaBoS) library. Numerical implementations based on previous equation of motion for solids are led in a non-intrusive manner so as to present results with an easy and flawless reproducibility. A new designed Lattice Boltzmann Method for Solids (LBMS) is exhibited through few key algorithms showing the overall operation plus the major improvements. Efficiency, robustness and accuracy of the proposed approach are illustrated and contrasted with a commercial Finite Element Analysis (FEA) software. Obtained results reveal a considerable potential concerning static and further dynamic simulations involving solid constitutive laws within the LBM formalism