Mechanics of Self-Similar Hierarchical Adhesive Structures Inspired by Gecko Feet - Structural Interfaces and Attachments in Biology - page 207

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