Page 93 - The Combined Finite-Discrete Element Method

76 CONTACT DETECTION

1 2
1 2
6 0 3 6 0 3
5 4
5 4

Figure 3.3 Typical dynamic problem.

For instance, there is a whole class of contact algorithms routinely employed with finite
element static systems involving contact. Most of these algorithms can handle only prob-
lems where the relative motion of contacting boundaries is restricted. Contact detection
is performed only once. Thus, the CPU performance of such contact detection algorithms
is not very important.
Real problems where contact detection is a big issue are dynamic problems, comprising
large numbers of discrete elements that are free to move significantly. Contact detection
itself can take a considerable proportion of the total CPU time required to analyse such
problems (over 60% in some cases).
In this context, when developing the contact detection algorithm, it is important to:

• Minimise the CPU requirements, i.e. total detection time T defined as the total CPU
time needed to detect all couples close to each other.
• Minimise the total memory (RAM) requirements M, expressed in terms of the total
memory size as a function of the total number of discrete elements N and pack-
ing density.

• Maximise performance expressed in terms of rate of M and T change with change in
packing density.

In this chapter, a number of contact detection algorithms currently available are described
in detail. However, the list of contact detection algorithms covered in this chapter is far
from complete, although it does represent different types of contact detection algorithms
that have been or are used to speed up the CPU intensive combined finite-discrete simula-
tions. Some of the algorithms described are suited for dense packs, while others perform
better with loose packs. Dense packs of discrete elements are characterised by:

• discrete elements being close to each other, and
• most of the physical space being occupied by discrete elements.

Loose packs of discrete elements are characterised by:

• discrete elements being far from each other, and
• most of the physical space is not occupied by discrete elements, i.e. is empty.

Towards the end of this chapter, the Munjiza-NBS algorithm, suited for both dense and
loose packs or systems where the density of the pack changes with time, is also presented
in detail, together with the recently developed Williams-C-grid algorithm. For the sake