Biomedical Engineering Reference
In-Depth Information
under cyclic loading as the internal structure of the tissue changes. As
water is lost through the “wringing out effect,” the tissue is less relaxed.
Similarly, there is a known decrease in relaxation with larger strains, also
likely due to a decrease in hydration. Alternatively, the decrease in the
rate of creep with increasing load is suspected to be due to more fibers
being recruited initially with larger loads, which ultimately decreases
the creep response.
In another example, cartilage is a low-friction, avascular, load-bearing
tissue, which can also exhibit a highly viscoelastic response and large
deformations. It is a triphasic material with a porous matrix made of type
II collagen, proteoglycans, and extracellular matrix, along with 70% to
90% without water and ions. Its flow-dependent viscoelasticity is mostly
due to its low permeability. Compact bone can be described as a matrix of
Haversian sites and hollow osteons embedded in ground substance, which
acts as cement lines between the osteons. When subjected to extended peri-
ods of stress, there is slippage along the cement lines and the ground sub-
stance is understood to behave in a viscous manner. Detailed models have
been developed to explain the features of such processes, especially at large
deformations, but are too complex to consider here.
additional problems
PROBLEM 4.6
Figure 4.16 (left curves) shows the stress versus time response for two
constrained strain-versus-time experiments (right curves). Answer the
following questions (yes or no):
1. Can curves
A
and
B
(stress versus time) result from experiments on
the same material?
2. Is
t
min
less than
t
1
for case
A
?
3. Does curve
A
(upper) display stress relaxation?
4. Could a compliance curve derived from case
A
yield the spectrum
of retardation times,
L
(
t
)?
5. If a strain of 0.025 were applied in a time =
t
1
/2, at a constant rate,
as in case
A
, would the peak stress be 20 MPa?
A
50
0.02
B
σ
ε
A
(MPa)
B
0.01
t
0
t
1
t
2
t
0
t
1
t
2
Time
FIGUre 4.16
stress and strain versus time (Problems 4.5 and 4.6).
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