document: The Discrete Element Method applied to spheres is well established as a reasonably realistic tool, in a wide range of engineering disciplines, for modelling packing and flow of granular materials; Asmar et al. [8] describes the fundamentals of this method as applied by code developed in-house at Nottingham; since these are widely documented the details are not reproduced here, simply a summary. It applies an explicit time stepping approach to numerically integrate the translational and rotational motion of each particle from the resulting forces and moments acting on them at each timestep. The inter-particle and particle wall contacts are modelled using the linear spring–dashpot–slider analogy. Contact forces are modelled in the normal and tangential directions with respect to the line connecting the particles centres. Particle elastic stiffness is set so sphere “overlap” is not significant and moderate contact damping is applied. Particle cohesion can also be modelled but is assumed to be negligible in the current study. The translational and rotational motion of each particle is modelled using a half step leap-frog Verlet numerical integration scheme to update particle positions and velocities. Near-neighbour lists are used to increase the computational efficiency of determining particle contacts and a zoning method is used each time the list is composed; that is the system is divided into cubic regions, each particle centre is within one zone, and potential contacting particles are within the same or next-door neighbour zones. Full details are given in Asmar et al. [8].
doc_bio_tags: O B I I O O B O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O B I O B I I I O O B O O O B O B O O O O O O O O O B O O O O O O B I I B I O O O O O O O O O O O O O O O B I B O O O O O B O O O O O O B I O O B O O O O O O O O O O O O O O O O B I I I O O B O O O O O O O O O O O O O B O O B O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O B O O O O O O O B I O O O O O O O O O O O O O O O O O
extractive_keyphrases: contact damping contact forces contacting particles discrete element method explicit time stepping approach forces granular materials linear spring–dashpot–slider analogy moments numerically integrate particle particles centres sphere spheres translational and rotational motion velocities zoning method
abstractive_keyphrases: half step leap-frog verlet numerical integration scheme inter-particle and particle wall contacts modelling packing and flow of granular materials near-neighbour lists particle centre particle cohesion particle contacts particle elastic particle elastic stiffness particle positions sphere “overlap”