Page 83 - The Combined Finite-Discrete Element Method

66 PROCESSING OF CONTACT INTERACTION

35
30
Legend:
× 1.0e+04 20 Penalty = 1.0e+05
25
Penalty = 7.0e+05
Penalty = 1.0e+06
Energy 15 Penalty = 1.0e+07

10
5
0
0 0.005 0.01 0.015 0.02 0.025
Time (s)

Figure 2.33 Energy balance for impact of the moving tetrahedron against a fixed tetrahedron.

−12.5
−12 Legend:
× 1.0e+2 −11.5 Penalty = 1.0e+07
Penalty = 1.0e+05

−11
Momentum −10.5

−10
−9.5
0 0.005 0.01 0.015 0.02 0.025
Time (s)
Figure 2.34 Momentum balance for impact of a tetrahedron with initial velocity against a tetra-
hedron at rest but free to move.

or ‘created’, irrespective of the size or geometry of the overlap of discrete elements
in contact.
The same simulations shown above are repeated with a bottom tetrahedron being ini-
tially at rest, but free to move. The top tetrahedron moves with an initial velocity of
550 m/s, while the bottom tetrahedron is at rest, and starts moving under the impact of
the top tetrahedron.
It can be observed that both energy and momentum balance are preserved, regardless of
the penalty used, as shown in Figures 2.34 and 2.35. This time, both tetrahedra move, as
illustrated by the motion sequence obtained using penalty p = 1e + 7 Pa, which is shown
in Figure 2.36.
Energy balance is especially important when discrete elements are confined so that
repeated contact-contact release occurs. When discrete elements are closely packed
together, these contact-contact release situations cannot be avoided. If numerical