Mechanics of Self-Similar Hierarchical Adhesive Structures Inspired by Gecko Feet - Structural Interfaces and Attachments in Biology - page 212

One might note that ( 10.27 ) implies an infinite adhesion strength in the limit of
' ¼ 0. This is caused by the uniaxial tensile stress that we have assumed. Actually,
the limit ' ¼ 0 should be characterized as sliding under an applied shear stress. If,

instead of pulling, we apply a remote shear stress s xy , the critical shear stress

becomes

p
CðD 22 cos 2

W ad

= pa

ðs xy Þ cr ¼

q (10.32)

y þ D 11 sin 2 yÞ

which can be reduced to

2

p

W ad =pa

ðs xy Þ cr ¼

p

CD 11

(10.33)

when D 22 D 11 and y ¼ 30 , and to

p

W ad

= pa

ðs xy Þ cr ¼ p

CD 11

(10.34)

when D 22 ¼ D 11 for the isotropic case. The results of ( 10.33 ) and ( 10.34 ) are shown
by the star symbols in Fig. 10.9b .

10.4.4 Directional Adhesion Strength of an Attachment Pad:
Numerical Simulation

To further verify the principle of orientation-controlled adhesion switch via strong
elastic anisotropy, we have also performed numerical simulations of the adhesion of
a strongly anisotropic attachment pad (mimicking the hairy structured tissue on
gecko's feet) via a general-purpose finite element code Tahoe (http://tahoe.ca.
sandia.gov) with specialized cohesive surface elements for modeling adhesive
interactions between two surfaces. The constitutive relation for the cohesive surface
elements is specified in terms of a relation between the traction and separation
across the contact interface. Tahoe supports a number of traction-separation laws
including the Tvergaard-Hutchinson law [ 50 ] and the Xu-Needleman law [ 51 ].
In present simulations, we adopt the Tvergaard-Hutchinson law based on the
following interaction potential

FðlÞ¼d cn ð l

0 'ðlÞ d l

(10.35)

where