Page 56 - The Combined Finite-Discrete Element Method

INTRODUCTION 39

Figure 2.2a Impenetrability condition imposed using pinballs placed on the boundary of dis-
crete elements.

while the total amount of recovered kinetic energy after contact release is proportional to

2
δ C (2.13)

As
2 2
δ C >δ B (2.14)
the final total energy is greater than the initial total energy.
An example of an attempt to simplify contact kinematics related procedures is a so-
called pinball algorithm, which is among the simplest slideline algorithms. Its core idea is
to embed pinballs into a surface, and therefore enforce the impenetrability condition only
to pinballs. Difficulties can arise from the large number of pinballs needed to discretise
the surface, or an unrealistic distribution of contact forces due to the discrete nature of
pinballs, Figure 2.2a.
Pinballs can produce unrealistic behaviour of the system, as shown in Figure 2.3, where
even with smooth surfaces and the absence of friction, sliding of contact surfaces over
each other is difficult.

Figure 2.3 Sliding of surface A over smooth surface B is made numerically difficult due to the
introduction of pinballs.