Page 69 - The Combined Finite-Discrete Element Method

52 PROCESSING OF CONTACT INTERACTION

0.18
0.17 D
0.16 C Legend
Kinetic energy [GNm] 0.14 A
0.15
B
0.13 B
C
D
0.12
0.11
0.1
0.09
0.08 A
0.07
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Time (ms)
Figure 2.17 Kinetic energy of beam shaped heaps A, B, C and D as a function of time.

All four heaps start at the same initial kinetic energy, which is equal to the initial kinetic
energy of the projectile. As the impact occurs, the projectile slows down, and contact
between individual fragments results in some of kinetic energy of the system being taken
as the potential energy, due to overlapping fragments in contact. This temporary reduction
in kinetic energy is largest for heap A and smallest for heap D. In fact, in terms of kinetic
energy, there is a gradual convergence from heap A to heap D, as though the kinetic
energy for heap A is a crude approximation of the kinetic energy for heap D.
For all four heaps, as the transient contacts are released due to the fragments mov-
ing away from each other, the initial kinetic energy of the system is restored. Contacts
have therefore resulted in some of the kinetic energy being transformed into potential
energy, and finally, the transfer of potential energy into kinetic energy, due to contacts
being released. Thus, the contact interaction algorithm as described in this chapter has
preserved the energy for all four heaps, regardless of the number of contacts, duration
of those contacts, or the size of overlap between fragments in contact, which is the
result theoretically predicted. This is also demonstrated by a bar-shaped heap, shown in
Figure 2.19. The heap comprises identical triangular rigid particles closely packed with
each other in such a way that no contact force is generated.
All fragments of the heap move at the same initial velocity (v = 500 ms) towards a
fixed rigid obstacle of a triangular shape, Figure 2.18.
The problem is solved for two heaps: heap A consists of 1280 identical rigid fragments
of triangular shape, while heap B consists of 5120 rigid fragments (Figure 2.19).
The transient motion of heap B due to the impact is shown in Figure 2.20. The initial
impact results in contact between the rigid obstacle and heap fragments. Due to the contact

2m 1m

10 m

Figure 2.18 A heap of rigid fragments moving towards a rigid obstacle.