Page 82 - The Combined Finite-Discrete Element Method

POTENTIAL CONTACT FORCE IN 3D 65

Figure 2.31 Motion sequence of a tetrahedron with initial velocity impacting on the fixed tetra-
hedron–obtained using a penalty term p = 1.0e + 6Pa.

Figure 2.32 Motion sequence of a tetrahedron with initial velocity impacting on a fixed tetrahe-
dron–obtained using a penalty term p = 1.0e + 7Pa.

The motion sequence shown in Figure 2.29 corresponds to a very small penalty. Thus,
penetration is far from small. In fact, the tetrahedra ‘go through’ each other. Irrespective
of this, the energy balance is preserved, as shown in Figure 2.33.
The increased value of penalty makes the moving tetrahedron bounce from the fixed
tetrahedron, although only after a large overlap, as can be observed from Figure 2.30.
In Figure 2.31 the motion sequence for a slightly larger penalty term is shown. This
time the penetration is still large. However, the moving tetrahedron ‘bounces’ from the
fixed tetrahedron. Regardless of a large penetration, the energy balance is preserved, as
shown in Figure 2.33.
In Figure 2.32 an even larger penalty is employed, resulting in further reduced penetra-
tion and eventual bouncing off of discrete elements from each other. Again, as Figure 2.33
shows, energy balance is preserved. It is evident that, for any value of penalty term, some
of the kinetic energy is transformed into potential energy due to overlap (penetration).
After the contact release, this energy is recovered and transformed back into kinetic
energy. Thus, at all stages the energy balance is preserved, i.e. no energy is either ‘lost’