Biomedical Engineering Reference
In-Depth Information
k c(t)
1
0.8
0.6
0.4
0.2
0.5
1
1.5
2
2.5
3
Fig. 1.12
The creep function. This is a plot of the spring constant k times the creep function c(t),
on the abscissa, against the dimensionless time ratio
t
/
t
F
on the ordinate. See (
1.10
). The five
curves are for different ratios of
t
x
/
t
F
. Since 0
< t
x
/
t
<
1 the plots, from
bottom
to
top
are for
F
values of
t
x
/
t
F
equal to 0.1, 0.3, 0.5, 0.7 and 0.9
t
F
is indeed the characteristic relaxation
time of the deflection at constant load. Plots of the creep function
c
(
t
) (multiplied
by the spring constant
k
) against the dimensionless time ratio
t
/
From this result it may be seen that
t
F
for different
ratios of
t
x
/
t
F
are shown in Fig.
1.12
. Because the values of
t
x
/
t
F
are restricted by
0
t
F
equal to 0.1, 0.3, 0.5, 0.7, and 0.9. The relaxation function for the standard linear
solid is given by
< t
x
/
t
F
<
1, the plots in Fig.
1.12
are, from bottom to top, for values of
t
x
/
t
x
1
e
t=t
x
h
t
F
r
ð
t
Þ¼
k
1
þ
ð
t
Þ:
(1.11)
t
x
is indeed the characteristic relaxation time
of the load at constant deflection. Plots of the relaxation function
r
(
t
), divided by the
spring constant
k
, against the dimensionless time ratio
t
/
From this result it may be seen that
t
x
for different ratios of
t
x
/
t
F
are shown in Fig.
1.13
. The values of
t
x
/
t
F
employed are 0.1, 0.3, 0.5, 0.7, and
0.9; the same values as in Fig.
1.12
.
Higher order lumped parameter models are obtained by combining the lower
order models described above. There is a strong caveat against the process of
combining elementary lumped parameter models to build higher order models.
The caveat is that the number of parameters increases and defeats the advantage
of simplicity of the lumped parameter model. Thus, the standard linear solid
considered is the most reasonable of the spring and dashpot models as a first
approximation of the force-deformation-time behavior of real materials.
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