Biomedical Engineering Reference
In-Depth Information
followed by a discussion on harmonic excitation, a technique that is often used to
determine material properties of visco-elastic materials.
5.2
Viscous behaviour
It is not surprising that biological tissues do not behave purely elastically, since a
large percentage of most tissues is water. The behaviour of water can be charac-
terized as 'viscous'. Cast in a one-dimensional format, viscous behaviour during
elongation (as in a fibre) may be represented by
1
d
dt
,
F
=
c
η
(5.1)
where
c
η
is the damping coefficient in [ Ns] and
d
/
dt
measures the rate of change
of the length of the fibre. Mechanically this force-elongational rate relation may
be represented by a dashpot (see Fig.
5.3
). Generally:
1
d
dt
D
=
(5.2)
is called the rate of deformation, which is related to the stretch parameter
λ
. Recall
that
0
,
λ
=
(5.3)
such that
1
d
dt
=
1
λ
d
dt
D
=
.
(5.4)
Ideally, a fluid stretching experiment should create a deformation pattern as visu-
alized in Fig.
5.4
(a). In practice this is impossible, because the fluid has to be
spatially fixed and loaded, for instance via end plates, as depicted in Fig.
5.4
(b). In
this experiment a fluid is placed between two parallel plates at an initial distance
0
. Next, the end plates are displaced and the force on the end plates is mea-
sured. A typical example of a stretched filament is shown in Fig.
5.5
. Although
this seems to be a simple experiment, it is rather difficult to perform in practice.
l
F
F
Figure 5.3
Mechanical representation of a viscous fibre by means of a dashpot.
