Biomedical Engineering Reference
In-Depth Information
The model in the right portion of Figure 4.12, with suitable values
for the stiffnesses or viscosities for each body, would fully describe this
behavior. The large dashpot and the frictional bodies connected with
slack ties on the left account for the preconditioning strain. On the right,
the spring elements are shown as engaging after discrete strains have
taken place. This is necessary to account for the concave-upward shape
of the stress-strain curves. This model is very simplified; to account for
the detailed shape of the loading curves, a large number of disconnected
spring bodies would be required.
Compliance
The reciprocal of a modulus is a
compliance.
The letter
J
is usually used
as a symbol for compliance. The compliance expresses the strain that
results from a unit of stress.
Thus, for an elastic-plastic material:
J
= 1/
E
= ε/σ
and for a viscoelastic material:
J
(
t
) = ε/σ
If a creep experiment is performed for a linear viscoelastic material
and paired (obtained at the same time) values of stress and strain are
used to compute
J
(
t
), then a plot of
J
(
t
) versus the logarithm of time yields
some interesting properties. Such an experiment is shown in Figure 4.13.
The compliance starts at a low constant value (
J
U
) and increases to a
high constant value (
J
R
). These are called, respectively, the
unrelaxed
and
relaxed compliances
and are the reciprocals of the unrelaxed and
relaxed moduli.
J
R
σ
J
(
t
)
Time
J
U
ε
t
min
t
max
Time (log)
FIGUre 4.13
the compliance curve.
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