Page 65 - The Combined Finite-Discrete Element Method

48 PROCESSING OF CONTACT INTERACTION

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Figure 2.11 Predicted transient motion sequence for heap A.

from the point of impact acquiring velocity and moving apart from each other–thus the
packing of the heap becomes looser. The actual analysis did not make use of the initial
symmetry of the problem. The problem as a whole was analysed instead, and the motion
of all 80 fragments, together with interaction among the fragments, was traced. Contact
forces were evaluated at each time step, while the central difference explicit time march-
ing scheme was employed to calculate the new velocity fields and new nodal coordinates.
It is worth noting that after the considerable movement of the individual fragments, the
symmetry of the system is still preserved.
The transient motion of heap B due to the impact of a rigid projectile is shown in
Figure 2.12. Again, the initial impact induces significant disturbance close to the middle
section of the heap. Through the interaction of individual rigid fragments, this disturbance
is spread toward the edges of the heap. The additional constraint of small support-like
triangles being fixed to the ground restricts the fragments closest to these supports. The
problem consisting of 320 rigid fragments is characterised by initial symmetry, and after
the impact and considerable movement of the fragments, the symmetry is preserved. This
is despite the fact that no symmetry is taken into account during analysis, and the problem
being analysed as a whole, i.e. by considering simultaneous transient motion of each of
the 320 interacting fragments.
The motion sequence for the heap C is shown in Figure 2.13. Again, as the projectile
hits the centre of the heap, the fragments close to the point of impact are accelerated.
However, this time the total number of fragments is much larger (1280), and each fragment
is therefore much smaller in comparison to the size of the projectile. The projectile
therefore gets ‘submerged’ among the fragments of the heap, and the subsequent motion
of the heap fragments at the initial stages reassembles a projectile going into a liquid.