Many recently synthesized materials feature aligned arrays or bundles of carbon nanotubes (CNTs) whose mechanical properties are partially determined by the van der Waals interactions between adjacent tubes. Of particular interest in this paper are instances where the resulting interaction between a pair of CNTs often produces a forklike structure. The mechanical properties of this structure are noticeably different from those for isolated individual CNTs. In particular, while one anticipates buckling phenomena in the forked structure, an adhesion instability may also be present. New criteria for buckling and adhesion instabilities in forklike structures are presented in this paper. The criteria are illuminated with a bifurcation analyses of the response of the forklike structure to applied compressive and shear loadings.

References

References
1.
Treacy
,
M. M. J.
,
Ebbesen
,
T. W.
, and
Gibson
,
J. M.
,
1996
, “
Exceptionally High Young’s Modulus Observed for Individual Carbon Nanotubes
,”
Nature
,
381
(
6584
), pp.
678
680
.10.1038/381678a0
2.
Baughman
,
R. H.
,
Zakhidov
,
A. A.
, and
de Heer
,
W. A.
,
2002
, “
Carbon Nanotubes—The Route Toward Applications
,”
Science
,
297
(
5582
), pp.
787
792
.10.1126/science.1060928
3.
Christensen
,
A.
,
Jacob
,
J.
,
Richards
,
C.
,
Bahr
,
D.
, and
Richards
,
R.
,
2003
, “
Fabrication and Characterization of a Liquid-Metal Micro-Droplet Thermal Switch
,”
12th International Conference on
Solid-State Sensors
, Boston, June 8–12,
Actuators and Microsystems
(
TRANSDUCERS
), Vol.
2
, pp.
1427
1430
.10.1109/SENSOR.2003.1217043
4.
Zhang
,
T.
,
Mubeen
,
S.
,
Myung
,
N. V.
, and
Deshusses
,
M. A.
,
2008
, “
Recent Progress in Carbon Nanotube-Based Gas Sensors
,”
Nanotechnology
,
19
(
33
), p.
332001
.10.1088/0957-4484/19/33/332001
5.
Oakley
,
W
.,
2007
, “
E-Beam Hard Disk Drive Using Gated Carbon Nano Tube Source and Phase Change Media
,”
24th IEEE Conference on Mass Storage Systems and Technologies
(
MSST 2007
), San Diego, CA, Sept. 24–27, pp.
245
250
.10.1109/MSST.2007.4367980
6.
McCarthy
,
M. A.
,
Liu
,
B.
,
Donoghue
,
E. P.
,
Kravchenko
,
I.
,
Kim
,
D. Y.
,
So
,
F.
, and
Rinzler
,
A. G.
,
2011
, “
Low-Voltage, Low-Power, Organic Light-Emitting Transistors for Active Matrix Displays
,”
Science
,
332
(
6029
), pp.
570
573
.10.1126/science.1203052
7.
Chen
,
B.
,
Gao
,
M.
,
Zuo
,
J.
,
Qu
,
S.
,
Liu
,
B.
, and
Huang
,
Y.
,
2003
, “
Binding Energy of Parallel Carbon Nanotubes
,”
Appl. Phys. Lett.
,
83
(
17
), pp.
3570
3571
.10.1063/1.1623013
8.
Zhou
,
W.
,
Huang
,
Y.
,
Liu
,
B.
,
Hwang
,
K. C.
,
Zuo
,
J. M.
,
Buehler
,
M. J.
, and
Gao
,
H.
,
2007
, “
Self-Folding of Single- and Multiwall Carbon Nanotubes
,”
Appl. Phys. Lett.
,
90
(
7
), p.
073107
.10.1063/1.2535874
9.
Cranford
,
S.
,
Yao
,
H.
,
Ortiz
,
C.
, and
Buehler
,
M. J.
,
2010
, “
A Single Degree of Freedom ‘Lollipop’ Model for Carbon Nanotube Bundle Formation
,”
J. Mech. Phys. Solids
,
58
(
3
), pp.
409
427
.10.1016/j.jmps.2009.11.002
10.
Torabi
,
H.
,
Radhakrishnan
,
H.
, and
Mesarovic
,
S. D.
,
2014
, “
Micromechanics of Collective Buckling in CNT Turfs
,”
J. Mech. Phys. Solids
,
72
, pp.
144
160
.10.1016/j.jmps.2014.07.009
11.
Sauer
,
R. A.
, and
Li
,
S.
,
2007
, “
An Atomic Interaction-Based Continuum Model for Adhesive Contact Mechanics
,”
Finite Elem. Anal. Des.
,
43
(
5
), pp.
384
396
.10.1016/j.finel.2006.11.009
12.
Falvo
,
M. R.
,
Clary
,
G. J.
,
Taylor
,
R. M.
,
Chi
,
V.
,
Brooks
,
F. P
,
Washburn
,
S.
, and
Superfine
,
R.
,
1996
, “
Bending and Buckling of Carbon Nanotubes Under Large Strain
,”
Nature
,
389
(
6651
), pp.
582
584
.10.1038/39282
13.
Tong
,
T.
,
Zhao
,
Y.
,
Delzeit
,
L.
,
Kashani
,
A.
,
Meyyappan
,
M.
, and
Majumdar
,
A.
,
2008
, “
Height Independent Compressive Modulus of Vertically Aligned Carbon Nanotube Arrays
,”
Nano Lett.
,
8
(
2
), pp.
511
515
.10.1021/nl072709a
14.
Volkov
,
A. N.
,
Shiga
,
T.
,
Nicholson
,
D.
,
Shiomi
,
J.
, and
Zhigilei
,
L. V.
,
2012
, “
Effect of Bending Buckling of Carbon Nanotubes on Thermal Conductivity of Carbon Nanotube Materials
,”
J. Appl. Phys.
,
111
(
5
), p.
053501
.10.1063/1.3687943
15.
Won
,
Y.
,
Gao
,
Y.
,
Panzer
,
M. A.
,
Xiang
,
R.
,
Maruyama
,
S.
,
Kenny
,
T. W.
,
Cai
,
W.
, and
Goodson
,
K. E.
,
2013
, “
Zipping, Entanglement, and the Elastic Modulus of Aligned Single-Walled Carbon Nanotube Films
,”
Proc. Natl. Acad. Sci. U.S. A.
,
110
(
51
), pp.
20426
20430
.10.1073/pnas.1312253110
16.
Sudak
,
L. J.
,
2003
, “
Column Buckling of Multiwalled Carbon Nanotubes Using Nonlocal Continuum Mechanics
,”
J. Appl. Phys.
,
94
(
11
), pp.
7281
7287
.10.1063/1.1625437
17.
Wang
,
Q.
,
Duan
,
W. H.
,
Liew
,
K. M.
, and
He
,
X. Q.
, “
Inelastic Buckling of Carbon Nanotubes
,”
Appl. Phys. Lett.
,
90
(
3
), p.
033110
.10.1063/1.2432235
18.
Shima
,
H.
,
2011
, “
Buckling of Carbon Nanotubes: A State of the Art Review
,”
Materials
,
5
(
1
), pp.
47
84
.10.3390/ma5010047
19.
Majidi
,
C.
,
O’Reilly
,
O. M.
, and
Williams
,
J. A.
,
2012
, “
On the Stability of a Rod Adhering to a Rigid Surface: Shear-Induced Stable Adhesion and the Instability of Peeling
,”
J. Mech. Phys. Solids
,
60
(
5
), pp.
827
843
.10.1016/j.jmps.2012.01.015
20.
Majidi
,
C.
,
O’Reilly
,
O. M.
, and
Williams
,
J. A.
,
2013
, “
Bifurcations and Instability in the Adhesion of Intrinsically Curved Rods
,”
Mech. Res. Commun.
,
49
(
0
), pp.
13
16
.10.1016/j.mechrescom.2013.01.004
21.
Hoffman
,
K.
, and
Manning
,
R.
,
2009
, “
An Extended Conjugate Point Theory With Application to the Stability of Planar Buckling of an Elastic Rod Subject to a Repulsive Self-Potential
,”
SIAM J. Math. Anal.
,
41
(
2
), pp.
465
494
.10.1137/080731803
22.
O’Reilly
,
O. M.
, and
Peters
,
D. M.
,
2012
, “
Nonlinear Stability Criteria for Tree-Like Structures Composed of Branched Elastic Rods
,”
Proc, R. Soc. Ser. A
,
468
(
2137
), pp.
206
226
.10.1098/rspa.2011.0291
23.
Love
,
A. E. H.
,
1927
,
A Treatise on the Mathematical Theory of Elasticity
,
4th ed.
,
Cambridge University Press
,
Cambridge, UK
.
24.
Faruk Senan
,
N. A.
,
O’Reilly
,
O. M.
, and
Tresierras
,
O. M.
,
2008
, “
Modeling the Growth and Branching of Plants: A Simple Rod-Based Model
,”
J. Mech. Phys. Solids
,
56
(
10
), pp.
3021
3036
.10.1016/j.jmps.2008.06.005
25.
O’Reilly
,
O. M.
,
2007
, “
A Material Momentum Balance Law for Rods
,”
J. Elasticity
,
86
(
2
), pp.
155
172
.10.1007/s10659-006-9089-6
26.
Reid
,
W. T.
,
1972
,
Riccati Differential Equations
,
Academic
,
New York.
.
27.
Boyd
,
S.
, and
Vandenberghe
,
L.
,
2004
,
Convex Optimization
,
Cambridge University Press
,
New York
.
28.
Autumn
,
K.
,
Liang
,
Y. A.
,
Hsieh
,
S. T.
,
Zesch
,
W.
,
Chan
,
W. P.
,
Kenny
,
T. W.
,
Fearing
,
R.
, and
Full
,
R. J.
,
2000
, “
Adhesive Force of a Single Gecko Foot-Hair
,”
Nature
,
405
(
6787
), pp.
681
685
.10.1038/35015073
29.
Autumn
,
K.
,
Sitti
,
M.
,
Liang
,
Y. A.
,
Peattie
,
A. M.
,
Hansen
,
W. R.
,
Sponberg
,
S.
,
Kenny
,
T. W.
,
Fearing
,
R.
,
Israelachvili
,
J. N.
, and
Full
,
R. J.
,
2002
, “
Evidence for van der Waals Adhesion in Gecko Setae
,”
Proc. Natl. Acad. Sci. U.S.A.
,
99
(
19
), pp.
12252
12256
.10.1073/pnas.192252799
30.
Zeng
,
X.
, and
Li
,
S.
,
2011
, “
Multiscale Modeling and Simulation of Soft Adhesion and Contact of Stem Cells
,”
J. Mech. Behav. Biomed. Mater.
,
4
(
2
), pp.
180
189
.10.1016/j.jmbbm.2010.06.002
31.
Chen
,
B.
,
Wu
,
P.
, and
Gao
,
H.
,
2008
, “
Hierarchical Modelling of Attachment and Detachment Mechanisms of Gecko Toe Adhesion
,”
Proc. R. Soc. London, Ser. A
,
464
(
2094
), pp.
1639
1652
.10.1098/rspa.2007.0350
32.
Tian
,
Y.
,
Pesika
,
N.
,
Zeng
,
H.
,
Rosenberg
,
K.
,
Zhao
,
B.
,
McGuiggan
,
P.
,
Autumn
,
K.
, and
Israelachvili
,
J.
,
2006
, “
Adhesion and Friction in Gecko Toe Attachment and Detachment
,”
Proc. Natl. Acad. Sci. U.S.A.
,
103
(
51
), pp.
19320
19325
.10.1073/pnas.0608841103
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