Page 97 - The Combined Finite-Discrete Element Method

80 CONTACT DETECTION

b

a
b

a b

a

Figure 3.6 Identical bounding rectangles for 2D discrete elements.

2
box, the total CPU time is proportional to N . Thus, if the total number of discrete
elements is increased by 100 times, the total CPU time increases by 10,000 times. This
is a major problem with the direct checking approach, and the main reason why direct
checking based contact detection algorithms are almost never used in FEM/DEM codes.

3.3 FORMULATION OF CONTACT DETECTION PROBLEM FOR
BODIES OF SIMILAR SIZE IN 2D

As explained in the previous section, various bounding objects can be defined for each
discrete element, and then contact detection and checking for contact performed in terms
of these bounding objects.
Use of bounding boxes greatly simplifies the contact detection problem, and makes
contact detection algorithms based on bounding boxes more robust and more general. For
the sake of simplicity and clarity of explanation, in the rest of this chapter, the simplified
contact detection problem limited to two-dimensional space is defined as follows:
A set of discrete elements is given in a 2D space. Every discrete element is bounded
by a circle of the same diameter d. All discrete elements are contained inside the space
bounded by a square of the edge s (Figure 3.7). The task is to detect all discrete elements
that are close to each other so that the bounding circles either touch or overlap.

The contact detection algorithms considered in the following sections will assume a sim-
plified contact detection problem in 2D, unless otherwise stated. All the algorithms will
be explained in 2D for the sake of clarity. Towards the end of this chapter, an extension
to 3D will be given.
As demonstrated by the direct checking approach from the previous section, changing
the shape or size of the bounding box, or using different shapes and sizes of bounding
boxes, is a relatively simple task, which does not change the essence or the key pro-
cedures of any contact detection algorithm. Some contact detection algorithms are very
complex, and are not easy to explain. Different shapes and sizes of bounding boxes would
complicate the situation even further, making the explanation difficult to follow.