Biomedical Engineering Reference
In-Depth Information
where
EE
=
/(
1
−
ν
2
)
is the plane strain modulus of
the specimen, and
(
)
−
1
is the reduced modulus with
E
the plane strain
modulus of the diamond tip. (2) In case
E
is not known
a priori
, based on
the knowledge of
S
,
E
can be computed first via the Oliver-Pharr
approach for conical ind
e
nter
2
or the Fische
r
-Cripps sol
ut
ion for
spherical indenter.
92
Next,
E
can be obtained as
E
=
1/
E
+
1/
E
R
i
(
E
−
)
1
= −
, and
the Oliver-Pharr
2
or Fischer-Cripps
92
solution is reversed such that the
intrinsic
S
can be derived for conical or spherical indentation,
respectively.
Another important issue is to alleviate the data fluctuation measured
in an experiment by imposing proper theory as the guide. For example,
during a sharp indentation experiment, very often there is significant data
scattering of
S
even during the holding at the maximum load,
93
and
such fluctuation must be removed in order to obtain more reliable
material properties from the reverse analysis. Two approaches may be
undertaken: (1) Average the
S
reported by CSM during the entire period
of holding at maximum load. (2) According to the Oliver-Pharr method,
2
0
/
SA
should be independent of
h
(where
A
is the projected contact
area), and thus
0
Sh
should be roughly a constant during sharp
indentation (especially when
h
gets beyond a certain depth). Thus, the
averaged
0
Sh
(when the depth is above a certain threshold) can be used
in the reverse analysis. The second method may lead to more stable
results of the identified material properties from the reverse analysis. In
case of spherical indentation, from Ref. 92, for a given material
0
/
Sh
should be almost a constant during indentation. Therefore, the averaged
0
/
Sh
can be used to derive
S
at a particular depth.
In this chapter, we focus on the computational modeling of
indentation, with an emphasis of extracting the constitutive properties of
materials including biological materials. Presently, there are many open
questions regarding the factors contributing to the constitutive response
and cracking induced by indentation. Answers to these questions are of
fundamental value and can be greatly assisted by computational
modeling. A significant effort of computational modeling is to establish a
reliable reverse analysis approach, which will be employed to determine
various unknown material parameters from the experimental data
obtained by indentation tests. Once determined, the material properties
E
1/
E
1/
R
i
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