Biomedical Engineering Reference
In-Depth Information
an existing quasistatic load function to increase the amount of
information obtained from a single indentation test. For example, small-
amplitude sinusoidal loading superimposed on the holding segment of a
response of a viscoelastic material, giving the real and imaginary parts
of the complex modulus (
E
*(
is the sinusoidal loading
frequency; see Section 6.1.4 below). This mode of dynamic testing will
be discussed later in this chapter. First, we examine the elastic contact
mechanics expressions as a function of indenter tip shape.
) where
loading, (b) a trapezoidal load-hold-unload profile in which creep can be measured
during the holding period, and (c) exponential loading.
3. Elastic Contact
Much of the work on elastic contact originated with the work of Hertz
in the late 19
th
century.
8
An excellent overview is presented in the text
of Johnson.
4
The work of Hertz concerned the contact of two bodies with
effectively spherical profiles, in which an effective radius
R
is defined in
the context of the radii of the two bodies (
R
1
,
R
2
) as:
1
R
=
1
R
1
+
1
R
2
(5-2)
Similarly, the elastic modulus of the contact is defined by the series
combination of the plane strain moduli of the two bodies:
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