Discrete Element Simulation and the Contact Problem

This paper addresses the problem of contact detection in discrete element multibody dynamic simulations. This paper presents an overview of the problem and a detail description of a new object representation scheme called the discrete function representation (DFR). This representation is designed to reduce the computational cost of both contact detection and the more diicult problem of contact resolution. The scheme has a maximum theoretical complexity of order O(N) for contact resolution between bodies deened by N boundary points. In practice, the discrete element method constrains overlap between objects and the actual complexity is approximately O(p (N) giving a speedup of nearly 2 orders of magnitude over traditional algorithms for systems with more than 1000 objects. The technique is robust and is able to handle convex and concave object geometries, including objects containing holes. Examples of relatively large discrete element simulations in three dimensions are presented.