Highlights

This work is funded by the EPSRC of UK under grant No. GR/R87422 and GR/R92318. This support is gratefully acknowledged.

Keywords Modelling, Geometry, Computational geometry

Abstract This paper proposes an energy-based general polygon to polygon normal contact model in which the normal and tangential directions, magnitude and reference contact position of the normal contact force are uniquely defined. The model in its final form is simple and elegant with a clear geometric perspective, and also possesses some advanced features. Furthermore, it can be extended to a more complex situations and in particular, it may also provide a sound theoretical foundation to possibly unifying existing contact models for all types of (convex) objects.

1. Introduction

This paper presents a general polygon to polygon normal contact model in the context of the discrete element method (DEM). The DEM in the classical sense (Cundall and Strack, 1979) assumes that all discrete objects are rigid and that their behaviour is largely determined by the interaction laws specified for interelement contact. The contact interaction laws are normally developed within the framework of penalty methods which only approximately satisfies the contact displacement constraints, thereby allowing a small amount of overlap to occur.

Polygons are one of the basic geometric entities...