Page 67 - The Combined Finite-Discrete Element Method

50 PROCESSING OF CONTACT INTERACTION

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Figure 2.14 Second part of the predicted transient motion sequence for heap C.

The initial symmetry of the system is again preserved, despite the fact that no symmetry
was taken into account during analysis, i.e. the problem was analysed as a whole, and
motion of all 1280 fragments was traced at each time step.
Heap D consists of the smallest fragments. The size and shape of the heap remain
the same as in heaps A, B and C. Thus, the total number of closely packed fragments
is much larger–the heap consists of 5120 fragments, initially packed in such a way that
they touch, but no two fragments overlap each other and no contact force is generated.
First contact occurs after the projectile makes contact with fragments close to the centre
of the heap. The projectile penetrates the heap, and fragments in the heap are initially
extracted by the projectile. This results in fragments close to the point of impact moving
in the opposite direction of the projectile (Figure 2.15).
This initial contact is followed by contacts between the heap fragments. Thus, the
fragments move away from each other, reducing the average packing density of the heap.
This motion results in the shape of the heap being gradually changed until the projectile
finally goes through the heap (Figure 2.16). At this stage, the shape of the heap has
changed significantly, and individual fragments have acquired significant velocity, thus
the remaining contacts are released, and eventually, the projectile and fragments move at
a constant velocity. This time the initial symmetry of the system is in general preserved,
although localised loss of symmetry can be observed. However, it is worth noting that
the total number of individual fragments is relatively large, and the local bifurcation type
behaviour that is sensitive to rounding errors may occur (see Chapter 6).
The motion sequences obtained in some way converge from the motion sequence for
heap A to the motion sequence for heap D, and in some sense, the motion sequence of
heap A represents an approximation of the motion sequence of heap D, while the motion
sequence of heap D, by similar reasoning, approximates the motion sequence of a heap
consisting of an infinite number of infinitesimally small fragments. In all four heaps, the