Two-Dimensional Discrete Element Theory for Rough Particles

The surfaces of real sands are often rough and a discrete element modeling of rough granulates is very important to understand the behavior of real sands. This paper presents a two-dimensional discrete element method (DEM) to capture the roughness of particles. The model consists of two parts: equations governing the motion of rough particles and mechanical contact models controlling rough-contact behavior. The key point of the theory is that the assumption in the original DEM proposed by Cundell and Strack in 1979 that a pair of particles are in single-point contact, is here replaced by that the particles are in rough contact over a width. By making the idealization that the contact width is homogeneously distributed with a finite-number of the normal/tangential basic elements (BEs) (each BE is composed of spring, dashpot, slider, or divider), we relate the governing equations to local equilibrium and also establish a rolling contact model together with normal/tangential contact models. The three main features of the theory are that: two physical parameters need to be introduced in the theory to represent particle roughness in comparison to the original DEM; rolling stiffness, rolling viscous-damping parameter, and rolling strength due to roughness are all linked with their respective counterparts in the normal direction in a simple and complete formula through these two parameters; the equations governing motion of rough particles satisfy the local equilibrium condition. The present theory was incorporated into a DEM code to investigate the mechanical response of the material of different roughness, particularly the angle of internal friction ϕ. Twenty-four DEM simulations showed that ϕ predicted by the theory was significantly increased in comparison to the standard DEM prediction.