A Finite Element Model for Estimating Young-s Modulus of Carbon Nanotube Reinforced Composites Incorporating Elastic Cross-Links

The presence of chemical bonding between functionalized carbon nanotubes and matrix in carbon nanotube reinforced composites is modeled by elastic beam elements representing covalent bonding characteristics. Neglecting other reinforcing mechanisms in the composite such as relatively weak interatomic Van der Waals forces, this model shows close results to the Rule of Mixtures model-s prediction for effective Young-s modulus of a Representative Volume Element of composite for small volume fractions (~1%) and high aspect ratios (L/D>200) of CNTs.

[1] T.S. Gates, G.M. Odegard, S.J.V. Frankland, T.C. Clancy,
"Computational Materials: Multi-scale modeling and simulation of
nanostructured materials," Comp. Sci. Tech., vol. 65, 2005, pp. 2416-
[2] CY. Li, T-W. Chou, "Multiscale modeling of compressive behavior of
carbon nanotube/polymer composites," Comp. Sci. Tech., vol. 66, 2006,
pp. 2409-2414.
[3] K.I. Tserpes, P. Papanikos, G. Labeas, Sp. G. Pantelakis, "Multiscale
modelinf of tensile behavior of carbon nanotube-reinforced composites,"
Theor. Appl. Fract. Mech., vol. 49, 2008, pp. 51-60.
[4] K.T. Lau, "Interfacial bonding characteristics of nanotube/polymer
composites," Chem. Phys. Lett., vol. 370, 2003, pp. 399-405.
[5] G.D. Seidel, D.C. Lagoudas, "Micromechanical analysis of the effective
elastic properties of carbon nanotube reinforced composites," Mech.
Mater., vol. 38, 2006, pp. 884-907.
[6] J. Gou, Z. Liang, C. Zhang, B. Wang, "Computational analysis of singlewalled
carbon nanotube rope on molecular interaction and load transfer
of nanocomposites," Comp. Part B, vol. 36, 2005, pp. 524-533.
[7] V. Anumandla, R.F. Gibson, "A comprehensive closed form
micromechanics model for estimating the elastic modulus of nanotubereinforced
composites," Comp. Part A, vol. 37, 2006, pp. 2178-2185.
[8] S.J.V. Frankland, V.M. Harik, G.M. Odegard, D.W. Brenner, T.S. Gates,
"The stress-strain behavior of polymer-nanotube composites from
molecular dynamics simulation," Comp. Sci. Tech., vol. 63., No. 11,
2003, pp. 1655-1661.
[9] E.T. Thostenson, CY. Li, T-W. Chou, "Nanocomposites in context,"
Comp. Sci. Tech., vol. 65, 2005, pp. 491-516.
[10] S.B. Sinnot, "Chemical functionalization of carbon nanotubes," J.
Nanosci. Nanotech., Vol. 2, No. 2, 2002, pp. 113-123.
[11] S.J.V. Frankland, A. Caglar, D.W. Brenner, M. Gabriel, "Molecular
simulation of the influence of chemical cross-links on the shear strength
of carbon nanotube-polymer interfaces," J. Phys. Chem. B, vol. 106, No.
12, 2002, pp. 3046-3048.
[12] X.-L. Gao, K. Li, "A shear lag model for carbon nanotube-reinforced
polymer composites," Int. J. Solid. Struct., vol. 42, 2005, pp. 1649-1667.
[13] D.A Rey et al., "Carbon Nanotubes in Biomedical Applications,"
Nanotech. Law Business, Vol. 3, No. 3, Sep 2006, pp.263-292.
[14] CY. Li, T-W. Chou, "A structural mechanics approach for the analysis
of carbon nanotubes," Int. J. Solid. Struct., vol. 40, 2003, pp. 2487-2499.
[15] K.I Tserpes, P. Papanikos, "Finite element modeling of single-walled
carbon nanotubes," Comp. Part B, vol. 36, 2005, pp. 468-477.
[16] W.D. Cornell, et al., "A second generation force field for the simulation
of proteins, nucleic acids, and organic molecules," J. Am. Chem. Soc.,
vol 117, 1995, pp. 5179-5197
[17] W.L. Jorgensen, D.L. Severance, "Aromatic-aromatic interactions-free
energy profiles for the benzene dimmer in water chloroform and liquid
benzene," J. Am. Chem. Soc., vol 112, 1990, pp. 4768-4774.
[18] T.I. Zohdi, P. Wriggers, Introduction to Computational
Micromechanics. Berlin: Springer-Verlag, 2005, ch. 2.