Page 58 - The Combined Finite-Discrete Element Method

POTENTIAL CONTACT FORCE IN 2D 41

Concentrated
Distributed contact force
contact force

Contactor Contactor

Target Target

Figure 2.3a Distributed and concentrated contact force approach.

However, in practice large penalty terms are coupled with integration problems in the
temporal domain, and in practical applications the penalty function method is therefore
coupled with overlaps between bodies in contact.
When implemented into actual codes dealing with contact, the penalty function method
in general deals with either concentrated or distributed contact force (Figure 2.3a). The
concentrated contact force approach usually assumes nodal contact forces being a function
of penetration of individual contactor nodes into the target, while the distributed contact
force is in general evaluated from the shape and size of overlap between the contactor
and target.

2.3 POTENTIAL CONTACT FORCE IN 2D

The distributed contact force is adopted for two discrete elements in contact, one of which
is denoted as the contactor and the other as the target. When in contact, the contactor
and target discrete elements overlap each other over area S, bounded by boundary .
(Figure 2.4).
It is assumed that penetration of any elemental area dA of the contactor into the target
results in an infinitesimal contact force, given by

df = [gradϕ c (P c ) − gradϕ t (P t )]dA (2.17)

Γ ∩ b P , P c
t
b
c
t
dA
b ∩ b c df Γ c
t
Γ t
Figure 2.4 Contact force due to an infinitesimal overlap around points P c an P t .