Date of Award

Fall 2002

Document Type


Degree Name

Master of Science in Mechanical Engineering - (M.S.)


Mechanical Engineering

First Advisor

Anthony D. Rosato

Second Advisor

Bruce G. Bukiet

Third Advisor

N. Aubry


This work is aimed at developing a discrete element simulation that models the contact between elliptical grains or particles in granular materials. The goal is to implement an algorithm to carry out collision detection between ellipses as well as ellipsoidal objects. The practical issue here is that the real shape of macroscopic grains can be approximated better using elliptical curves than using spherical curves. In addition, the simulation model will also be valid for spheres, since these objects are special cases of ellipsoids.

An accurate contact detection algorithm was investigated by means of two different formulations. The first formulation determines the minimum distance of one ellipse with respect to another ellipse and vice versa and finds the two closest points. Then it analyzes the position of these two points. However, this formulation is not robust enough to determine all the contact detections tested. The first formulation fails in cases when the distance between centers is unrealistically close and the major and minor axes are large. The second formulation determines the overlap distance. This method was successful in each of the realistic cases tested. The second formulation, as well as the first formulation, fails in unphysical cases, i.e., the distance between the centers of the ellipses is much smaller than the size of the major and minor axes of the ellipses. The implementation of a contact force formulation with minimum overlap distance will remove any possibility that these cases occur.