The objective of this paper is to develop constitutive models to predict thermoelastic properties of carbon single-walled nanotubes using analytical, asymptotic homogenization, and numerical, finite element analysis, methods. In our approach, the graphene sheet is considered as a non-homogeneous network shell layer which has zero material properties in the regions of perforation and whose effective properties are estimated from the solution of the appropriate local problems set on the unit cell of the layer. Our goal is to derive working formulas for the entire complex of the thermoelastic properties of the periodic network. The effective thermoelastic properties of carbon nanotubes were predicted using asymptotic homogenization method. Moreover, in order to verify the results of analytical predictions, a detailed finite element analysis is followed to investigate the thermoelastic response of the unit cells and the entire graphene sheet network.

1.
Iijima
S.
,
1991
, “
Helical microtubules of graphitic carbon
,”
Nature
,
354
, pp.
56
58
.
2.
Ajayan, P. M., Schadler, L. S., and Braun, P. V., Nanocomposite Science and Technology, Wiley-VCH, Weinheim, 2003.
3.
Liu
J. P.
, “
Elastic Properties of Carbon Nanotubes and Nanoropes
,”
Physical Review Letters
, Vol.
79
, No.
7
,
1997
, pp.
1297
1300
.
4.
Treacy
M. M. J.
,
Ebbesen
T. W.
, and
Gibson
J. M.
, “
Exceptionally high Young’s modulus observed for individual nanotubes
,”
Nature
,
381
,
1996
, pp.
678
680
.
5.
V. M. Harik, “Ranges of Applicability for the Continuum-beam Model in the Constitutive Analysis of Carbon Nanotubes: Nanotubes or Nano-beams?,” NASA/CR-2001-211013 ICASE Report No. 2001-16, ICASE, Hampton, VA, 2001.
6.
M. S. Dresselhaus, G. Dresselhaus, and P. Avouris, Carbon Nanotubes: Synthesis, Structure, Properties, and Applications, Springer, New York, 2000.
7.
Kwon
Y. K.
,
Berber
S.
, and
Tomanek
D.
Thermal Contraction of Carbon Fullerenes and Nanotubes
,”
Physical Review Letters
, Vol.
92
, No.
1
,
2004
, pp.
015901
-
1
.
8.
Che
J.
,
Cagin
T.
and
Goddard
W. A.
, “
Thermal Conductivity of Carbon Nanotubes
,”
Nanotechnology
, Vol.
11
,
2000
, pp.
65
69
.
9.
Guseva
O.
,
Lusti
H. R.
, and
Gusev
A. A.
, “
Matching Thermal Expansion of Mica-Polymer Nanocomposites and Metals
,”
Modelling and Simulation in Materials Science and Engineering
, Vol.
12
,
2004
, pp.
101
106
.
10.
Maniwa
Y.
,
Fujiwara
R.
,
Kira
H.
,
Tou
H.
,
Kataura
H.
,
Suzuki
S.
,
Achiba
Y.
,
Nishibori
E.
,
Takata
M.
,
Sakata
M.
,
Fujiwara
A.
, and
Suematsu
H.
, “
Thermal Expansion of Single-Walled Carbon Nanotube (SWNT) Bundles: X-ray Diffraction Studies
,”
Physical Review B
, Vol.
64
,
2001
. pp.
1
3
.
11.
Lusti
H. R.
and
Gusev
A. A.
, “
Finite Element Predictions for the Thermoelastic Properties of Nanotube Reinforced Polymers
,”
Modelling and Simulations in Materials Science and Engineering
Vol.
12
,
2004
, pp.
S107–S119
S107–S119
12.
A. L. Kalamkarov, Composite and Reinforced Elements of Construction, John Wiley & Sons Ltd., NY, 1992.
13.
A. L. Kalamkarov and A. G. Kolpakov, Analysis, Design and Optimization of Composite Structures, John Wiley & Sons Ltd., NY, 1997.
14.
Kalamkarov
A. L.
,
Veedu
V. P.
, and
Ghasemi-Nejhad
M. N.
, “
Mechanical Properties Modeling of Carbon Single-Walled Nanotubes: An Asymptotic Homogenization Method
,”
Journal of Computational and Theoretical Nanoscience
, Vol.
2
, No.
1
,
2005
, pp.
124
131
.
15.
ANSYS Manual, ANSYS Inc. Canonsburg, PA, 2004.
16.
M. N. Ghasemi-Nejhad and D. Askari, “Mechanical Properties Modeling of Carbon Single-Walled Nanotubes: A Finite Element Method,” Journal of Computational and Theoretical Nanoscience, 2005 (in press).
This content is only available via PDF.
You do not currently have access to this content.