Biomedical Engineering Reference
In-Depth Information
Table 10.1
Calculated geometrical and mechanical properties of bottom-up designed fractal
gecko hair structure
nR
n
(m)
W
a
n
(J/m
2
)
N
n
f
L
n
(m)
'
n
S
n
(MPa)
F
n
(N)
Triangular
1 7.0
10
8
1.37
10
6
3.08
10
7
1.539
10
3
0.5260 0.01
20
2 3.78
10
6
2.86
10
4
4.73
10
4
2.2032
10
4
0.5169 0.15
10.52
3 7.81
10
4
7.9914
10
5
0.36
0.5079 8.26
5.44
10.43
4.80
10
3
0.5079 2.67
10
3
8.33
10
6
9.2685
10
7
4 0.98
2.76
5 1.32
10
4
1.55
10
9
0.5079 9.31
10
6
7.72
10
14
5.2558
10
10
1.4026
6 4.26
10
9
3.41
10
16
0.5079 7.72
10
11
4.06
10
25
2.4676
10
14
0.7123
7 9.39
10
16
2.11
10
26
0.5079 4.39
10
18
1.00
10
40
1.9399
10
19
0.3618
8 5.80
10
26
2.39
10
39
0.5079 7.0
10
27
1.94
10
59
6.5330
10
25
0.1837
Square
1 7.0
10
8
1.37
10
6
3.08
10
7
1.777
10
3
0.4555 0.01
20
2 4.37
10
6
3.46
10
4
5.47
10
4
2.7977
10
4
0.4477 0.13
9.11
3 1.10
10
3
1.1534
10
6
0.56
0.4398 6.49
4.08
15.50
1.06
10
4
0.4398 2.03
10
3
1.76
10
7
1.5865
10
8
4 1.7691
1.79
5 3.36
10
4
5.35
10
9
0.4398 7.47
10
6
2.80
10
15
1.1291
10
11
0.79
6 1.70
10
10
2.16
10
17
0.4398 7.33
10
11
3.16
10
26
7.1761
10
14
0.35
7 6.88
10
17
3.0
10
27
0.4398 5.72
10
18
2.27
10
41
8.4482
10
19
0.15
8 9.53
10
27
9.97
10
40
0.4398 1.53
10
28
1.91
10
61
4.8744
10
26
0.067
Hexagonal
1 7.0
10
8
1.37
10
6
3.08
10
7
2.309
10
3
0.3507 0.01
20
2 5.68
10
6
4.91
10
4
7.10
10
4
4.3203
10
4
0.3446 0.10
7.01
3 2.0
10
3
2.2486
10
6
1.25
0.3386 4.20
2.42
30.37
4.42
10
4
0.3386 1.24
10
3
6.90
10
7
4.2178
10
8
4 5.18
0.82
5 1.83
10
5
5.12
10
10
0.3386 5.02
10
6
2.91
10
16
4.5376
10
11
0.28
6 2.12
10
11
6.23
10
18
0.3386 6.66
10
11
1.32
10
28
5.0028
10
15
0.0938
7 2.57
10
19
3.75
10
29
0.3386 9.27
10
18
6.61
10
43
1.2276
10
21
0.0318
8 1.55
10
30
8.85
10
43
0.3386 6.40
10
28
8.14
10
64
1.8860
10
28
0.0108
remains almost constant in spite of several orders of magnitude change in body
mass [
38
]. How do we understand this from a mechanics point of view? Within
single species, it is easier to adopt the same design for single contact element and
simply multiply this strategy by increasing the adhesion pad size. This strategy is
limited, since eventually the adhesion pad becomes too large and flaw sensitive.
New species will have to emerge with more sophisticated structural hierarchy.
It seems that gecko only adopts a few levels of hierarchical fibrillar structures to
achieve robust adhesion. A question then is: why has nature not evolved more
hierarchical levels, and thus larger adhesion species heavier than gecko? A possible
answer to this question is addressed in the following section.
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