A theoretical analysis of the force models in discrete element method

This paper presents an investigation of the equilibrium, stability and pure rolling problems of a sphere moving on a flat plane with special reference to a few force models which are commonly used in the discrete element method (DEM) and here categorized into two types: with and without rolling friction. It is obtained that according to the models without rolling friction, the set of equilibrium states of the system is not asymptotically stable, which does not agree with the fact that the sphere with small initial tangential velocity, angular velocity and tangential displacement should eventually stop. The models also display that the sphere can roll on the plane without sliding only when both the tangential force and torque acting on the sphere are zero, which is not reasonable for a viscoelastic sphere moving on a hard plane. On the other hand, the models with rolling friction cannot describe the pure rolling motion of the sphere with any material properties. The results highlight the theoretical deficiency associated with the force models in DEM. Based on the findings, modified models are proposed to overcome the above problems.