Biomedical Engineering Reference
In-Depth Information
Table 10.2
Parameters used in FEM simulation
Isotropic case
E ¼
1
:
0 GPa,
n ¼
0
:
3
Anisotropic case
E
t
¼
0
:
1 MPa,
E
l
¼
1
:
0 GPa,
n
t
¼ n
l
¼
0
:
3,
m ¼
10 MPa,
y ¼
30
Parameters for Tvergaard-Hutchinson model
L
1
¼
0
26J/m
2
)
:
1,
L
2
¼
0
:
9,
s
max
¼
5
:
44 MPa,
d
cn
¼ d
ct
¼
1
:
687
m
m(
W
ad
¼
8
:
roughness), as shown in Fig.
10.10a
. A displacement-controlled load is applied on
the upper surface to make all the nodes on the upper surface have a uniform
translation. At a given translation, summation of all the nodal forces on the upper
surface gives the pulling force
F
with components
F
x
and
F
y
. The pulling angle is
then calculated via
' ¼
tan
1
ðF
y
=F
x
Þ
. Periodic boundary conditions are applied on
left and right sides. For comparison, both the isotropic case and the anisotropic
cases are considered. The material constants and potential parameters for each
simulation case are listed in Table
10.2
, where we adopt the calculated
S
3
and
W
ad
3
of the triangular hair pattern (see Table
10.1
) as the effective adhesion strength and
work of adhesion, respectively, in simulating the detachment process of the pad.
To illustrate the anisotropy-induced releasability of adhesion, Fig.
10.10b
plots
the normalized pull-off stress
F
c
ð'Þ=ðAs
max
Þ
as a function of the pulling angle
.
In the anisotropic case, saturation of adhesion strength is observed in the vicinity of
' ¼ y ¼
30
, corresponding to a plateau of the curve in the range of 20
<'<
'
40
.
If the pulling angle deviates from this range in either direction, the adhesion
strength decreases quickly to a lower plateau. This two-plateau adhesion strength
is ideal for rapid switch between attachment and detachment during animal move-
ment. The ratio between the maximum and minimum strengths reaches four for the
given geometry, giving rise to significant releasability. In contrast, for the isotropic
cases, no variation in pull-off force is observed as the pulling angle varies. There-
fore, we conclude that strong elastic anisotropy leads to releasable adhesion via an
orientation-controlled switch between strong and weak adhesion.
10.5 Conclusions
In this chapter, we discussed the basic principles of robust and releasable adhesion
in the hierarchical structures of gecko. The work has been inspired by comparative
studies of biological attachment systems in nature. For robust adhesion, we use a
bottom-up designed fractal hair structure as a model to demonstrate that hierarchi-
cal fibrillar structures can lead to robust adhesion at macroscopic scales. Barring
fiber fracture, we show that the fractal gecko hairs system can tolerate crack-like
flaws without size limit. However, in practice, as the adhesion strength is enhanced
by structural hierarchy, fiber fracture ultimately becomes the dominant failure
mechanism and places an upper bound on the size scale of flaw tolerant adhesion.
An optimal design is to introduce an appropriate number of hierarchical levels so
that the adhesion interface and the hairs have similar strength levels. For releasable
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