A General Contact Theory for Non-spherical Particles

Abstract

A general contact theory for modelling normal contact of non-spherical particles in discrete element modelling is proposed in the current work. It is established based on two principles: (1) the energy-conservation and (2) geometrical considerations, and presented in four theorems. The theorem of Energy Conserving Contact Model states that the normal force must be the gradient of a potential field, when such a potential function is defined, a complete normal contact model will be completely determined. When the potential is a function of the contact volume, a special contact model with clear geometric meanings is developed as described by the theorem of Contact Volume Based Model. Then the contact of any axi-symmetric objects is also addressed through two theorems that reveal a fundamental relationship between the contact point and the contact normal, and offer a simple approach to determine the normal direction based on the contact point and vice versa.