Abstract
AbstractThe Lattice Boltzmann Method (LBM), e.g. in [1] and [2], can be interpreted as an alternative method for the numerical solution of certain partial differential equations that is not restricted to its origin in computational fluid mechanics. The interpretation of the LBM as a general numerical tool allows to extend the LBM to solid mechanics as well, see e.g. [3], which is concerned with the simulation of elastic solids under simplified deformation assumptions, and [4] as well as [5] which propose LBMs for the general plane strain case. In previous works on a LBM for plain strain such as [5], the treatment of practically relevant boundary conditions like Neumann and Dirichlet type boundary conditions is not the main focus and thus periodic conditions or absorbing layers are specified to simulate numerical examples. In this work, we show how Neumann and Dirichlet type boundary conditions are implemented in our LBM for plane strain from [4].
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