Lattice spring methods for arbitrary meshes in two and three dimensions

Abstract

SummaryThe computation of elastic continua is widely used in today's engineering practice, and finite element models yield a reasonable approximation of the physically observed behaviour. In contrast, the failure of materials due to overloading can be seen as a sequence of discontinuous effects finally leading to a system failure. Until now, it has not been possible to sufficiently predict this process with numerical simulations. It has recently been shown that discrete models like lattice spring models are a promising alternative to finite element models for computing the breakdown of materials because of static overstress and fatigue. In this paper, we will address one of the downsides of current lattice spring models, the need for a periodic mesh leading to a mesh‐induced anisotropy of material failure in simulations. We will show how to derive irregular cells that still behave as part of a homogeneous continuum irrespectively of their shape and which should be able to eliminate mesh‐induced anisotropy. In addition, no restraints concerning the material stiffness tensor are introduced, which allows the simulation of non‐isotropic materials. Finally, we compare the elastic response of the presented model with present lattice spring models using mechanical systems with a known analytical stress field. Copyright © 2016 John Wiley & Sons, Ltd.