Page 90 - The Combined Finite-Discrete Element Method

3

Contact Detection

3.1 INTRODUCTION

Large-scale combined finite-discrete element simulations involve contact of a large number
of separate bodies, each body being represented by a single discrete element. It is evident
from Chapter 2 that processing of contact interaction involves the summation of contact
forces over contacting couples comprising target and contactor elements:
n n

f = f ij (3.1)
i=1 j=1
Thus, processing contact interaction for all possible contacts would involve a total num-
2
ber of operations proportional to N ,where N is the total number of discrete elements
comprising the problem.
This would be very CPU intensive, and would limit application of the combined finite-
discrete element method to simulations comprising a very small number (a few thousand)
discrete elements. To reduce CPU requirements of processing contact interaction, it is
necessary to eliminate couples of discrete elements that are far from each other and are
not in contact. A set of combined finite-discrete element procedures designed to detect
discrete or finite elements that are close to each other is usually called a contact detection
algorithm, or sometimes a contact search algorithm.
The contact detection algorithm must be:

• robust,
• CPU efficient,
• RAM efficient, and
• easy to implement.

The robustness of a contact detection algorithm means that it has to detect all those
couples of discrete elements that are actually in contact. In addition, it has to eliminate
most of the couples of discrete elements that are not in contact. It has to perform these
tasks irrespective of how the discrete elements are in positions relative to each other.
CPU efficiency means that the total CPU time spent on detecting all the contacting
couples must be as short as possible. The total CPU time is measured in terms of the

The Combined Finite-Discrete Element Method A. Munjiza
 2004 John Wiley & Sons, Ltd ISBN: 0-470-84199-0