Modelling transient stresses in dynamically loaded elastic solids using the Lattice Boltzmann Method

Abstract

AbstractIn solids subjected to transient loading, inertial effects and S‐ or P‐wave superposition can give rise to stresses which significantly exceed those predicted by quasi‐static models. It pays to accurately predict such stresses – and the failures induced by them – in fields from mining to automotive safety and biomechanics. This, however, requires costly simulations with fine spatial and temporal resolutions.The Lattice Boltzmann Method (LBM) can be used as an explicit numerical solver for certain appropriately formulated conservation laws [1]. It encodes information about the field variables to be simulated in distribution functions, which are modified locally and propagated across a regular lattice. As the LBM lends itself to finely discretised simulations and is easy to parallelise [2, p.55], it is an intriguing candidate as a solver for dynamic continuum problems.Recently, Murthy et al. [3] and Escande et al. [4] adopted LBM algorithms to model isotropic, linear elastic solids. We extended these algorithms using local boundary rules that allow us to model arbitrary‐valued Dirichlet and Neumann boundaries. Here, we illustrate applications of the LBM for solids and the proposed additions by way of a simple numerical example – a glass pane subject to a sudden impact load.