Mechanics of Carbon Nanotubes: A Continuum Theory Based on Interatomic Potentials


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It is commonly believed that continuum mechanics theories may not be applied at the nanoscale due to the discrete nature of atoms. We developed a nanoscale continuum theory based on interatomic potentials for nanostructured materials. The interatomic potential is directly incorporated into the continuum theory through the constitutive models. The nanoscale continuum theory is then applied to study the mechanical deformation and thermal properties of carbon nanotubes, including (1) pre-deformation energy; (2) linear elastic modulus; (3) fracture nucleation; (4) defect nucleation; (5) electrical property change due to mechanical deformation; (6) specific heat; and (7) coefficient of thermal expansion. The nanoscale continuum theory agrees very well with the experiments and atomistic simulations without any parameter fitting, and therefore has the potential to be utilized to complex nanoscale material systems (e.g., nanocomposites) and devices (e.g., nanoelectronics).



Key Engineering Materials (Volumes 340-341)

Edited by:

N. Ohno and T. Uehara




H. Q. Jiang et al., "Mechanics of Carbon Nanotubes: A Continuum Theory Based on Interatomic Potentials", Key Engineering Materials, Vols. 340-341, pp. 11-20, 2007

Online since:

June 2007




[1] S. Iijima: Nature Vol. 354 (1991), p.56.

[2] T.W. Ebbesen and P.M. Ajayan: Nature Vol. 358 (1992), p.220.

[3] A. Thess, R. Lee, P. Nikolaev, H.J. Dai, P. Petit, J. Robert, C.H. Xu, Y.H. Lee, S.G. Kim, A.G. Rinzler, D.T. Colbert, G.E. Scuseria, D. Tomanek, J.E. Fischer and R.E. Smalley: Science Vol. 273 (1996), p.483.

DOI: 10.1126/science.273.5274.483

[4] P.G. Collins, M.S. Arnold and P. Avouris: Science Vol. 292 (2001), p.706.

[5] T. W. Tombler, C. Zhou, L. Alexseyev, J. Kong, H. Dai, L. Liu, C. S. Jayanthi, M. Tang and S. -Y. Wu: Nature Vol. 405 (2000), p.769.

DOI: 10.1038/35015519

[6] D.W. Brenner: Phys. Rev. B Vol. 42 (1990), p.9458.

[7] P. Zhang, Y. Huang, P.H. Geubelle, P.A. Klein and K.C. Hwang: Int. J. Solids Struct. Vol. 39 (2002), p.3893.

[8] H. Jiang, P. Zhang, B. Liu, Y. Huang, P.H. Geubelle, H. Gao and K.C. Hwang: Comp. Mater. Sci. Vol. 28 (2003), p.429.

[9] P. Zhang, H. Jiang, Y. Huang, P.H. Geubelle and K.C. Hwang: J. Mech. Phys. Solids Vol. 52 (2004), p.977.

[10] E.B. Tadmor, R. Phillips and M. Ortiz: Langmuir Vol. 12 (1996), p.4529.

[11] E.B. Tadmor, G.S. Smith, N. Bernstein and E. Kaxiras: Phys. Rev. B Vol. 59 (1996), p.235.

[12] D.H. Robertson, D.W. Brenner and J.W. Mintmire: Phys. Rev. B Vol. 45 (1992), p.12592.

[13] C.F. Cornwell and L.T. Wille: Solid State Commun. Vol. 101 (1997), p.555.

[14] C. Goze, L. Vaccarini, L. Henrard, P. Bernier, E. Hernandez and A. Rubio: Synthetic Met. Vol. 103 (1999), p.2500.

[15] B.I. Yakobson, M.P. Campbell, C.J. Brabec and J. Bernholc: Comp. Mater. Sci. Vol. 8 (1997), p.341.

[16] M.B. Nardelli, B.I. Yakobson and J. Bernholc: Phys. Rev. Lett. Vol. 81 (1998), p.4656.

[17] M.B. Nardelli, B.I. Yakobson and J. Bernholc: Phys. Rev. B Vol. 57 (1998), p. R4277.

[18] B.I. Yakobson: Phys. Rev. Lett. Vol. 72 (1998), p.918.

[19] H. Jiang, X. -Q. Feng, Y. Huang, K.C. Hwang and P.D. Wu: Comput. Methods Appl. Mech. Engrg. Vol. 193 (2004) p.3419.

[20] J. Song, H. Jiang, D. -L. Shi, X. -Q. Feng, Y. Huang, M. -F. Yu and K.C. Hwang: Int. J. Mech. Sci. (in press).

[21] B. Liu, H. Jiang, H.T. Johnson and Y. Huang: J. Mech. Phys. Solids Vol. 52 (2004), p.1.

[22] H. Jiang, B. Liu, Y. Huang and K.C. Hwang: J. Eng. Mater-T. Vol. 126 (2004), p.265.

[23] H. Jiang, Y. Huang and K.C. Hwang: J. Eng. Mater-T. Vol. 127 (2005), p.408.

[24] D. Chandler: Introduction to Modern Statistical Mechanics (Oxford University Press, Oxford, 1987).

[25] B.H. Billings and D.E. Gray: American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

[26] H. Gao and P.A. Klein: J. Mech. Phys. Solids Vol. 46 (1998), p.187.

[27] P.A. Klein, J.W. Foulk, E.P. Chen, S.A. Wimmer and H. Gao: Theor. Appl. Fract. Mec. Vol. 37 (2001), p.99.

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