A novel discrete model for granular material incorporating rolling resistance

This paper presents a novel two-dimensional (2D) discrete model for granular materials with rolling resistance. The salient features of our formulation are: it consists of a geometrically derived kinematical model, physically based mechanical contact models and locally equilibrated equations governing the motion of the rigid particles; only one additional parameter δ needs to be introduced in the model when compared with the standard discrete element method (DEM). In the study, precise definitions of pure sliding and pure rolling were proposed, and a decomposition of a general contact displacement was given in terms of these rolling and sliding components which are then linked to energy dissipation. The standard DEM assumption that grains are in contact at discrete points was here replaced by the assumption that grains are in contact over a width. By making the idealization that the grain contact width is continuously distributed with normal/tangential basic elements, we established a rolling contact model together with normal/tangential contact models, and also related the governing equations to local equilibrium. As an example of its application, the present model was incorporated into a DEM code to study the angle of internal friction ϕ of the material. Fifty-four DEM simulations showed that ϕ predicted by the novel model was increased in comparison to the standard DEM prediction, and may be closer to the values observed experimentally provided that the δ-ϕ relationship established in this paper was used.