Biomedical Engineering Reference

In-Depth Information

The relative significance of fiber fracture can be measured by a comparison

between
s

max

n

and the effective adhesion strength
S
n
at the
n
-th hierarchical level. If

max

s

n
>S
n
, adhesion failure is regarded as the dominant issue and further increase in

hierarchical levels can be considered. On the other hand, if
s

max

n
<S
n
, fiber fracture

is regarded as the dominant issue, hence an upper limit on the hierarchical design.

Taking

n
and
S
n
for the fractal hair

structures constructed above. As shown in Fig.
10.7
, for triangular and square fiber

layout, only fibers within the first two levels satisfy the condition
s

G
f
¼
5J/m
2
and
E
f
¼
1 GPa, we compare
s

max

n
>S
n
; for the

hexagonal layout, this condition is satisfied for the first three levels. Hence,

although there is no upper bound for flaw tolerant adhesion via fractal hairs design,

crack-like flaws in the hairs themselves would impose a practical limit for the

usefulness of this strategy. Of course, above conclusions are based on the properties

of keratin, which is the material of gecko's attachment system. Therefore, unless

new structural protein is formed, gecko seems to stand near the limit of evolution.

max

10.4 Releasable Adhesion

For geckos and insects, robust adhesion alone is insufficient for survival as these

animals also need to move swiftly on walls and ceilings; the reversibility of

attachment is just as important as the attachment. A conceivable strategy for

reversible adhesion is to design an orientation-controlled switch between attach-

ment and detachment, with adhesion strength varying strongly with the direction of

pulling. An ideal scenario of robust and releasable adhesion is that the adhesion

strength would be maintained near the theoretical strength when pulled in some

range of directions, but then dramatically reduced when pulled in another range of

directions. The switch between attachment and detachment can thus be accom-

plished simply by changing the pulling angles (e.g., by exerting different muscles).

Some known examples of anisotropic adhesion systems in which the pull-off force

varies strongly with the direction of pulling include an elastic tape on substrate

[
5
,
21
,
40
] and a single seta of gecko sticking on a wall [
2
,
7
]. Here we show that

such behavior can actually be generalized to three-dimensional elastic solids as

long as there is sufficiently strong elastic anisotropy.

10.4.1 Directional Adhesion Strength of an Elastic Tape

For an elastic tape adhering on a substrate, as shown in Fig.
10.8a
, Kendall [
40
]

showed that the critical force required to peel the tape off the substrate can be

written as

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