Page 22 - The Combined Finite-Discrete Element Method

A TYPICAL PROBLEM OF COMPUTATIONAL MECHANICS OF DISCONTINUA 5

Figure 1.2 Gravitational deposition of identical spheres of diameter d = 2.635 mm; Left: initial
pack; Right: randomly perturbed pack before the start of deposition, i.e. at time t = 0s.

position. Due to energy dissipation, eventually the velocity of all particles is zero
and the pack is at the state of rest – which is also the state of static equilibrium. Thus,
through dynamic governing equations taking into account dynamic equilibrium and
through contact and the motion of individual particles, static equilibrium of the pack
is achieved.
In Figures 1.2–1.6, such deposition sequence of a pack comprising identical spheres of
diameter d = 2.635 mm is shown. As explained earlier, the total volume of the solid
deposited is V = 9.150e−03 m3. Thus, the pack comprises 955,160 identical spheres.
The maximum theoretical density for packs comprised of identical spheres is given by
√
π 18
= 0.7405
ρ = ∼ (1.5)
18
A density profile obtained using gravitational deposition is normalised using this theoret-
ical density. Density profiles for different packs are shown in Figure 1.7. Initially (solid
line), the particles are almost uniformly distributed over the box; the density is only
slightly larger at the bottom of the box than at the top.
The motion of the particles under gravity gradually increases density at the bottom of
the pack and decreases density at the top of the pack, making the upper parts of the box
empty. As the particles settle, the pack gets denser. At the state of rest (dashed line),
almost uniform density over most of the pack is achieved, with rapid density decrease
towards the top of the pack.