Biomedical Engineering Reference
In-Depth Information
the distance between these two interfaces,
s
, and a change in
s
measured
by the displacement gauge is recognized as the load-point displacement
conjugate to the load,
F
, measured by the load cell. The indenter
(environment) imposes one of
s
or
F
, and this is then the independent
variable in a test, and the system reacts leading to a change in
F
or
s
, and
this latter is then the dependent test variable. Hidden from view (from a
thermodynamic perspective) are the changes in the system and its
internal variables leading to the reaction. In particular, adhesive and
indentation interactions between the tip and the surface, quantified by the
internal tip-surface separation variable,
w
, and deformation responses of
the spring, quantified by the internal spring extension, (
s
w
), determine
the relationship between the changes in the independent and dependent
variables, and whether in fact an equilibrium (
F
,
s
) configuration exists
or can be attained.
The whole point of the above considerations is that while it is
F
and
s
that are measured and it is the (
F
,
s
) relationship that determines the
engineering performance of bodies in contact, it is the underlying (
F
,
w
)
contact relationship mediated by the (
F
,
s
−
w
) spring relationship that
determines what is observed and that provides scientific insight into the
bulk and surface properties of the body materials.
Let us consider a typical indentation contact as measured by a
displacement-controlled (
s
is the independent variable) IIT device to
examine these interrelationships. As a specific example, we will consider
a contact between a cylindrical flat-punch tip of radius
a
and a flat
surface. Both tip and surface are linearly elastic materials and have no
surface force interactions. Force and position will be taken as positive
when directed along the outward normal to the surface. An indentation
cycle begins with
s
large enough such that the tip and the surface are out
of contact and
F
is thus zero. If
s
is reduced so that the tip contacts
(indents) the surface, the spring is compressed, the tip contacts the
surface with a fixed circular contact perimeter, and the force required to
maintain the system in equilibrium,
F
< 0. The relative displacements of
the spring and tip-surface contact comprising the value of
s
at this force
depend on the relative stiffness of the two components,
k
S
and
k
a
,
−
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