Page 106 - The Combined Finite-Discrete Element Method

SCREENING CONTACT DETECTION ALGORITHM 89

Central
cell

Neighbouring
cells

Figure 3.18 Contact check mask for discrete elements mapped to the central cell.

contact for a particular discrete element from the central cell is reduced to a direct check
with discrete elements from either central or neighbouring cells.
In fact, it is enough to check against the discrete elements from cells shown in
Figure 3.18. This is because all cells containing a discrete element are in turn considered
to be central cells.
Contact detection described above involves only integerisation of current coordinates
of the centre for each discrete element. In addition, the total number of algebraic oper-
ations per discrete element does not depend upon the total number of discrete elements
comprising the system.
The total number of algebraic operations for mapping of all discrete elements onto the
cells is given by
n 1 = (2 additions + 1 division)N (3.27)

Thus, the total number of algebraic operations for detecting all contacts is proportional
to the total number of discrete elements, i.e.

n n ∝ N (3.28)

The total CPU time is also proportional to the total number of discrete elements. In
other words, if the total number of discrete elements is increased by tenfold, the total CPU
time will also increase by tenfold. Note that this was not the case with binary tree based
search. This algorithm is therefore much more efficient in its use of CPU time than the
binary tree based search. However, there is a problem to be solved. The algorithm is based
on the mapping of discrete elements onto identical cells. This mapping somehow has to
be represented in the memory of a computer. Depending on the representation of this
mapping, a whole family of contact detection algorithms can be devised. These include
the screening contact detection algorithm, sorting contact detection algorithm, Munjiza-
NBS contact detection algorithm and the Williams-C-Grid contact detection algorithm,
all described in the following sections.

3.6 SCREENING CONTACT DETECTION ALGORITHM FOR
DISCRETE ELEMENTS OF SIMILAR SIZE

The simplest way of representing the mapping of discrete elements onto identical cells is
to use one integer number per cell. The total number of integer numbers is equal to the