Biomedical Engineering Reference
In-Depth Information
infinitesimal perturbation of either
a
or
h
leads to an irreversible non-
equilibrium decrease (6) in
a
and increase in
P
until both
P
= 0 and
a
= 0
and the state (1) is regained (the sphere has “pulled-off” the surface). The
work performed by the actuator during the full adhesive indentation
Table 4-1. The salient points of the JKR response.
Contact
Radius
Load
Displacement
Comments
The quiescent point; zero load
adhered state
2
4/3
2
2/3
0
-8/9
The snap-on state under
displacement control
(4/3)
2/3
0
The pull-off state under load
control
-1
-1
1
The pull-off state under
displacement control
-9
1/3
(1/3)
2/3
-5/9
A contact sequence under load control is similar and transitions in
control are possible as well. For example, a sphere may be “placed” on
the surface under displacement control as above, reaching the stable
equilibrium condition (2), and then “let go” such that the system is now
characterized by a load-controlled non-equilibrium
P
= 0 condition. The
contact radius increases, following the non-equilibrium
P
= 0 line until
the quiescent point is reached (the sphere has snapped on to the surface
under load control).
The JKR model shares with the considerations of the logarithmic
potential a simplicity that allows the roles of the various factors
influencing the system to be calculated in closed-form analyses. In the
case of the logarithmic potential the factors were the tip-surface
interaction potential and the deformation potential of the probe spring,
which allowed the snap-on phenomenon to be studied. In the case of the
JKR model the factors were the surface energy of the tip-surface
interface and the elastic deformation energy of the tip and surface, which
allowed the snap-on, quiescent, indentation, and pull-off phenomenon to
be studied. In both cases, the models are probably too simple to describe
real adhesive indentation contacts exactly, although the JKR model does
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