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International Applied Mechanics

, Volume 42, Issue 1, pp 19–31 | Cite as

Three-dimensional theory of stability of a carbon nanotube in a matrix

  • A. N. Guz
Article

Abstract

The three-dimensional theory of stability of a carbon nanotube (CNT) in a polymer matrix is presented. The results are obtained on the basis of the three-dimensional linearized theory of stability of deformable bodies. Flexural and helical (torsional) buckling modes are considered. It is proved that the helical (torsional) buckling modes occur in a single CNT (the interaction of neighboring CNTs is neglected) and do not occur in nanocomposites (the interaction of neighboring CNTs is taken into account)

Keywords

nanocomposites CNT polymer matrix compression stability three-dimensional theory 

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References

  1. 1.
    M. Born and K. Huang, Dynamic Theory of Crystal Lattices, Oxford (1954).Google Scholar
  2. 2.
    A. N. Guz, “On setting up a stability theory of unidirectional fibrous materials,” Int. Appl. Mech., 5, No. 2, 156–162 (1969).MathSciNetGoogle Scholar
  3. 3.
    A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kiev (1971).Google Scholar
  4. 4.
    A. N. Guz, Stability of Elastic Bodies under Finite Strains [in Russian], Naukova Dumka, Kiev (1973).Google Scholar
  5. 5.
    A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kiev (1986).Google Scholar
  6. 6.
    A. N. Guz, Mechanics of Compressive Failure of Composite Materials [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
  7. 7.
    A. N. Guz (editor-in-chief), Mechanics of Composite Materials [in Russian], Vols. 1–4, Naukova Dumka, Kiev (1993), Vols. 5–12, A.S.K., Kiev (2003).Google Scholar
  8. 8.
    D. W. Brenner, “Empirical potential for hydrocarbons for use in simulating the chemical vapour deposition of diamond films,” Phys. Rev., B.42, 9458–9471 (1990).ADSGoogle Scholar
  9. 9.
    Chunyu Li and Tsu-Wei Chou, “Elastic moduli of multi-walled carbon nanotubes and the effect of Van der Waals forces,” Composit. Sci. Technol., 63, 1517–1524 (2003).CrossRefGoogle Scholar
  10. 10.
    Chunyu Li and Tsu-Wei Chou, “A structural mechanics approach for the analysis of carbon nanotubes,” Int. J. Solid Struct., 40, 2487–2499 (2003).CrossRefGoogle Scholar
  11. 11.
    Chunyu Li and Tsu-Wei Chou, “Modelling of elastic buckling of carbon nanotubes by molecular structural mechanics approach,” Mech. Mater., 36, 1047–1055 (2004).CrossRefGoogle Scholar
  12. 12.
    S. Govindjee and J. L. Sackman, “On the use of continuum mechanics to estimate the properties of nanotubes,” Solid State Communications, 110, 227–230 (1999).CrossRefGoogle Scholar
  13. 13.
    A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin-Heidelberg-New York (1999).Google Scholar
  14. 14.
    A. N. Guz, “On one two-level model in the mesomechanics of compressive fracture of cracked composites,” Int. Appl. Mech., 39, No. 3, 274–285 (2003).MATHCrossRefGoogle Scholar
  15. 15.
    A. N. Guz and I. A. Guz, “Mixed plane problems of linearized mechanics of solids: Exact solutions,” Int. Appl. Mech., 40, No. 1, 1–29 (2004).MathSciNetCrossRefGoogle Scholar
  16. 16.
    A. N. Guz, A. A. Rodger, and I. A. Guz, “Developing a compressive failure theory for nanocomposites,” Int. Appl. Mech., 41, No. 3, 233–255 (2005).CrossRefGoogle Scholar
  17. 17.
    A. N. Guz and J. J. Rushchitsky, “Nanomaterials: On the mechanics of nanomaterials,” Int. Appl. Mech., 39, No. 11, 1271–1293 (2003).CrossRefGoogle Scholar
  18. 18.
    I. A. Guz and J. J. Rushchitsky, “Comparing the evolution characteristics of waves in nonlinearly elastic micro-and nanocomposites with carbon fillers,” Int. Appl. Mech., 40, No. 7, 785–793 (2004).CrossRefGoogle Scholar
  19. 19.
    I. A. Guz and J. J. Rushchitsky, “Theoretical description of a delamination mechanism in fibrous micro-and nanocomposites,” Int. Appl. Mech., 40, No. 10, 1129–1136 (2004).Google Scholar
  20. 20.
    Hui-Shen Shen, “Postbuckling prediction of double-walled carbon nanotubes under hydrostatic pressure,” Int. J. Solid Struct., 41, 2643–2657 (2004).MATHCrossRefGoogle Scholar
  21. 21.
    Y. Jin and F. G. Yuan, “Simulation of elastic properties of single-walled carbon nanotubes,” Composit. Sci. Technol., 63, 1507–1511 (2003).CrossRefGoogle Scholar
  22. 22.
    J. J. Liu and X. L. Chen, “Evaluation of effective material properties of carbon nanotube-based composites using a nanoscale representative volume element,” Mech. Mater., 35, 69–81 (2003).CrossRefGoogle Scholar
  23. 23.
    O. Lourie, D. M. Cox, and H. D. Wagner, “Buckling and collapse of embedded carbon nanotubes,” Phys. Rev. Letters, 81, No. 8, 1638–1641 (1998).CrossRefADSGoogle Scholar
  24. 24.
    G. M. Odegard, T. S. Gates, L. M. Nicholson, and K. E. Wise, “Equivalent-continuum modelling of nano-structured materials,” Composit. Sci. Technol., 62, 1869–1880 (2002).CrossRefGoogle Scholar
  25. 25.
    E. Saether, S. J. V. Frankland, and R. B. Pipes, “Transverse mechanical properties of single-walled carbon crystals. Part I: Determination of elastic moduli,” Composit. Sci. Technol., 63, 1543–1550 (2003).CrossRefGoogle Scholar
  26. 26.
    Q. Wang, “Effective in plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes,” Int. J. Solid Struct., 41, 5451–5461 (2004).MATHCrossRefADSGoogle Scholar
  27. 27.
    J. Wang and R. Pyrz, “Prediction of the overall moduli of layered silicate-reinforced nanocomposites. Part I: Basic theory and formulas,” Composit. Sci. Technol., 64, 925–934 (2004).CrossRefGoogle Scholar
  28. 28.
    M. A. Wilson, K. Kannangara, G. Smith, M. Simmons, and B. Raguse, Nanotechnology. Basic Science and Emerging Technologies, Chapman & Hall/CRC, Boca Raton-London (2002).Google Scholar
  29. 29.
    I. R. Xiao, B. A. Gama, and I. W. Gillespie, Jr., “An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes,” Int. J. Solid Struct., 42, 3075–3092 (2005).CrossRefGoogle Scholar
  30. 30.
    B. L. Yakobson, C. I. Brobec, and I. Bernhole, “Nanomechanics of carbon tubes: Instabilities beyond linear response,” Phys. Rev. Letters, 76, 2511–2514 (1996).CrossRefADSGoogle Scholar
  31. 31.
    P. Zhang, Y. Jiang, P. H. Geubelbe, and K. C. Hwang, “An atomistic-based continuum theory for carbon nanotubes: analysis of fracture nucleation,” J. Mech. Phys. Solids, 52, 977–998 (2004).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. N. Guz
    • 1
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKiev

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