Biomedical Engineering Reference
In-Depth Information
analogous to
Eq. 5-12
and where
D
is a damping coefficient. The real
and imaginary moduli can be calculated directly from
π
P
0
h
0
2
E
S
)
cosφ
(5-48)
= (1 − ν
2
A
C
π
P
0
h
0
2
E
L
)
sin
φ
(5-49)
=
(1
− ν
2
A
C
The derivations of these expressions and caveats concerning their use can
be found in other sources.
38-40
In practice, the typical experiment would
include a number of different measurements for different frequencies
(“frequency sweep”) and the evaluation of the real and imaginary parts
of the complex modulus as a function of frequency and potentially also
as a function of static (
P
max
) and dynamic (
P
0
) load levels.
6.2.
Poroelastic contact
Poroelasticity concerns the flow of fluid through a saturated porous
elastic solid.
41
Although the components (fluid, solid) themselves are
taken to be time-independent, the flow problem creates time-dependence
in the response. The basic elastic problem is augmented in poroelasticity
with two additional scalar variables, the pore pressure,
p
, and an
increment of fluid content,
, the change in fluid volume relative to a
control volume. The poroelastic framework considered here is for an
isotropic elastic porous material with elastic material properties shear
modulus,
G
, and Poisson's ratio,
. There are two other parameters to
characterize the fluid and the fluid-solid interactions, and
B
, which
are bounded between zero and unity. With the additional variables (
p
, )
and material constants (,
B
), the stress-strain (
ij
−
ij
) relationship
for elasticity is modified by the addition of a term including the pore
pressure (
p
ij
) to become:
2
G
ν
ε
kk
δ
ij
+ α
p
δ
ij
+
(5-50)
σ
ij
=
2
G
ε
ij
1
−
2
ν
ij
is the Kronecker delta.
26
A single additional scalar expression is
added to the six elastic equations to total seven constitutive equations:
where
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