Biomedical Engineering Reference
In-Depth Information
10
6
10
5
Membrane
Stretching
F
w
0
3
α
10
4
λ = 3 × 10
4
10
3
10
2
Plate
Bending
F
λ
= 350
10
1
α
w
0
λ = 85
10
0
10
-1
Indentation
F
α
w
0
3/2
10
-2
10
-2
10
-1
10
0
10
1
10
2
Shaft Displacement,
w
0
/ h
Figure 10-6. The multi-scale behavior of the shaft-loaded blister test. Loading is
dominated consecutively by indentation, plate bending, mixed bending-stretching, and
membrane-stretching. The data points (diamonds) are obtained by finite element analysis.
the sample in the first approximation for the empiricists, provided the
applied load falls in the
range indicated above.
Residual membrane stress and viscoelasticity can also be
incorporated into the solid-mechanics model. The biaxial tensile pre-
stress, σ
0
, causes the compliance of the sample membrane to decrease,
similar to strain-hardening. A rigorous derivation shows the mechanical
response to be
λ −
2
F
1
I
(
)
K
(
)
I
(
)
K
(
)
2
(10-18)
w
00
0
0 1
0
0 0
0
1
0
K
() g
0
00
2
b
I
(
)
0
0 1
0
0
0
b a
2
/
)
1/2
and
where
= 0.577216 is the Euler-Mascheroni
constant. The effect is that the bending asymptote shifts upwards
reminiscent of classical strain hardening. The stretching asymptote, on
the other hand, remains unchanged, because the increasing concomitant
β
0
= (
σ
κ
γ
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