Biomedical Engineering Reference
In-Depth Information
contact hardness (
H
c
=
P
max
/
A
c
). Typically, in commercial indentation
instruments the full procedure is carried out in the background, such that
the output to the instrument operator is simply the properties (
E
R
and
H
c
)
as a function of depth (
h
c
) assuming the frame compliance and area
functions were programmed into the instrument.
5. Elastic Contact of Complex Materials and Systems
The elastic solutions presented in Section 3 were for indentation of a
homogeneous isotropic elastic half-space. Before moving on to examine
more complicated material constitutive behavior, such as viscoelastic
materials, we will first briefly mention elastic indentation in three cases
that frequently arise in the context of biological tissues: anisotropic
materials, inhomogeneous (composite) materials and layered systems
(i.e. thin films on substrates). Unsupported membrane systems will be
considered in
Chapter 10
of this volume, and will therefore be excluded
from the current discussion.
5.1.
Anisotropic materials
Indentation of an anisotropic material has been considered in explicit
analytical formulations
15,16
and experimentally for bone.
17
The premise
is that the anisotropic indentation modulus,
M
, is defined where
M
is specific to the orientation of the anisotropic material being indented,
with the limiting case that
M
=
E
/(1 −
2
) for an isotropic material.
Analogous to the relationship between reduced (or plane strain) modulus
S
π
M
=
(5-17)
2
A
c
The indentation modulus
M
is defined in the context of the ratio of radii
modulus is a complicated integral expressions over components
B
ij
derived from the stiffness matrix (
C
ij
):
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