Page 105 - The Combined Finite-Discrete Element Method

88 CONTACT DETECTION

d/2 d/2

d/2

Centre of both the
cell and bounding
circle of discrete
d/2
element

Figure 3.16 Cells are large enough to contain a whole discrete element.

of the current coordinates of the centre of each discrete element:

int x i − x min
x i = 1 + Int (3.26)
d

int y i − y min
y i = 1 + Int
d

Step 2: Find discrete elements that may be in contact: it is worth noting that every single
discrete element can fit into a single cell in such a way that if the centre of a particular
discrete element coincides with the centre of the cell, no point of discrete element is
outside of the cell, as shown in Figure 3.16. Two discrete elements mapped onto cells
that share either nodes or edges (neighbouring cells) can be in contact. In addition, two
discrete elements mapped onto cells that share neither nodes nor edges (non-neighbouring
cells) cannot be in contact, as shown in Figure 3.17.
No discrete elements mapped onto the central cell in Figure 3.17 can be in contact to
discrete elements outside either the central cell or neighbouring cells. Thus, detection of

Central
cell
Neighbouring
cells

Figure 3.17 Cells neighbouring the central cell are marked. All other cells are non-neighbouring
cells.