Page 133 - The Combined Finite-Discrete Element Method

116 CONTACT DETECTION

The results obtained show that the total detection time is not dependent on packing
density, which changes from

1 1
1to i.e. from 1 to (3.68)
200 2 40,000

Example IV consists of N = 10,000 circular discrete elements of diameter D spaced
at distance 2D in the y-direction and at distance D and S in the x-direction (Figure 3.52).
For each given value of S, contact detection is performed 10 times, and the total CPU
time for all 10 detections of all contacts is recorded using profiled debugging version of
the code. The results are shown in Figure 3.53.
The numerical results shown above clearly demonstrate that the total detection time is
constant for a large range of packing densities. This is the case for all packs considered,
as theoretically predicted.
In summary:

• Memory requirements of the Munjiza-NBS algorithm are insignificant, and do not
change significantly with considerable changes in packing density.

• Total detection time for the Munjiza-NBS algorithm does not depend upon packing
density, a result confirmed by both theoretical investigations and numerical experiments.
• The relationship between the total detection time and the total number of discrete
elements comprising the problem is linear. This result is confirmed by both theoretical
investigations and numerical experiments.

Packing "D"

2D

2D

2D

D S S D

Figure 3.52 Example IV, packing D (A. Munjiza and K.R.F. Andrews, International Journal for
Numerical Methods in Engineering, 43/1). (Reproduced by permission of John Wiley & Sons, Ltd).