Lattice Boltzmann Simulation of Plane Strain Problems

The Lattice Boltzmann Method (LBM), e.g. in [3] and [4], can be interpreted as an alternative method for the numerical solution of partial differential equations. LBM is usually applied to solve fluid flows. However, interpretation a general tool, allows extend solid mechanics well. In this spirit, has been studied recent years. First publications [5], [6] present scheme dynamic behavior linear elastic under simplified deformation assumptions. For so-called anti-plane shear deformation, only non-zero displacement component governed by two-dimensional wave equation. work, existing equation extended more plane strain problems. algorithm reduces problem two separate equations volume dilatation rotation vector, respectively.