Mechanics of Self-Similar Hierarchical Adhesive Structures Inspired by Gecko Feet - Structural Interfaces and Attachments in Biology - page 200

Fig. 10.5 Bottom-up design scheme of a hierarchical fibrillar structure. At each level, the fibers
depend on smaller fibrils from the lower hierarchical levels as effective “adhesive bonds” with a
surface. Interestingly, the fibers themselves act as “adhesive bonds” for larger fibers from higher
hierarchical levels

length for multiple fiber bunching is no less than that given by ( 10.7 ). It seems that
the anti-bunching condition between two fibers is the most critical condition against
bunching involving multiple fibers.

10.3.4 “Fractal Gecko Hairs”: Bottom-Up Designed

Hierarchical Fibrillar Structures

Given that the work of adhesion can be increased to a larger value by adopting a
“hairy” structure [ 20 , 25 , 31 , 32 ], the critical length for flaw tolerant adhesion can also
be extended to a larger scale, according to ( 10.3 ). Meanwhile, the increase in work of
adhesion with each level of added hierarchy should be limited by the maximum length
of the fibers allowed by the anti-bunching condition. In other words, bunching
between fibers provides an upper limit on how much the flaw tolerant length scale
can be extended by one level of hierarchy. In order to achieve flaw tolerant adhesion at
macroscopic length scales, multiple levels of hierarchy may be needed. To demon-
strate the principle of flaw tolerance via structure hierarchy, we propose a “fractal
gecko hairs” model, in which a hierarchical fibrillar structure is made from multiple
levels of self-affine “brush” structures, as shown in Fig. 10.5 . In this fractal structure,
the tips of fibers at each level of hierarchy are assumed to be coated with a “brush”
structure consisting of smaller fibrils from one level below. The flaw tolerance and
anti-bunching conditions are applied to all hierarchical levels from bottom and up to
ensure robustness and stability at all levels. That is, the robustness principle of flaw
tolerance and the stability principle of anti-bunching are used to determine the fiber
geometry at different scales. The bottom-up construction of the desired hierarchical
structure is described in some detail below.