Reduction of discrete element models by Karhunen-Loève transform: A hybrid model approach

Abstract

The term "discrete element method" (DEM) in engineering science comprises various approaches to model physical systems by agglomerates of free particles. While shapes, sizes and properties of particles may vary, in most DEM models, particles are not confined by constraints, but subject to applied forces derived from potential fields and/or contact laws. This general approach allows for widespread use of DEM models for physical phenomena including gas dynamics, granular flow, fracture and impact analysis. However, its characteristic feature, combining particle restraints and forces into applied forces, does not only provide for flexible adaption of DEM to different physics, but also creates themost limiting restriction: Evaluation of the applied forces for each particle is computational expensive restraining the time sequence and sample size for numerical analyses. As an ansatz to circumvent this obstacle for a class ofDEMmodels, we propose a model order reduction method based on coherency in the dynamics of particles. While initial flexibility of DEM is conserved, computational effort can be reduced significantly. © The Author(s) 2009.