Biomedical Engineering Reference
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t = t
1
(σ = σ
0
)
t = t
0
(σ = 0)
1
1
2
2
L
K
L
H
L
O
t = t
0
(σ = σ
0
)
t > t
1
(ε = ε
1
)
1
1
2
2
L
L
K
L
H
L
K
L
H
FIGUre 4.9
the linear viscoelastic model: Kelvin unit connected end
to end (in series) with a spring/hooke body.
σ
0
σ
ε
ε
0
E
(
t
)
t
0
t
l
Time
FIGUre 4.10
the standard test of the linear viscoelastic model.
the external strain is set, the stress in the dashpot does not change, since
it is stressed by spring 2. However, as it continues to strain, the stress
in spring 2 decreases and a restraining stress is produced by additional
deformation of spring 1. Eventually, the stress in spring 1 is equal to the
stress in spring 2 (but not equal to zero), and internal deformation ceases.
If we compare the behavior of
E
(
t
) in Figure 4.10 with that for the
Maxwell unit (Figure 4.8) and the Kelvin unit (Figure 4.9), we can see
that it is much better behaved, never having either a zero value or an infi-
nite value. Its initial value, immediately after stress is applied but before
creep can take place, is called the
unrelaxed modulus
,
E
U
. Its final value,
after all possible internal stress relaxation has taken place, is called the
relaxed modulus
,
E
R
. In this case, as in the general case for viscoelastic
materials,
E
U
>
E
R
.
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