Advertisement

The Atomic-Scale Finite Element Method for Post-Buckling of Carbon Nanotubes

  • A. Y. T. Leung
  • Xiang Guo

Abstract

This paper employs atomic-scale finite element method to study axial-buckling of carbon nanotubes (CNTs). The computed energy curves agree well with molecular dynamics simulations. Both local and global buckling are achieved. The global buckling behavior of SWNT with a larger aspect ratio approaches gradually to that of a column described by Euler’s formula. For double-walled CNTs with smaller ratio of length to outer diameter, the local buckling behavior can be explained by conventional shell theory very well. The bending and torsion buckling of the CNTs is also investigated.

Key words

global buckling local buckling critical strain carbon nanotuibes atomic-scale finite elements 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Falvo MR, Clary GJ, Taylor RM II, Chi V, Brooks FP Jr, Washburn S, Superfine R. Bending and buckling of carbon nanotubes under large strain. Nature (London), 1997; 389: 582–584.CrossRefGoogle Scholar
  2. 2.
    Lourie O, Cox DM, Wagner HD. Buckling and collapse of embedded carbon nanotubes. Phys. Rev. Lett., 1998; 81: 1638–1641.CrossRefGoogle Scholar
  3. 3.
    Yakobson BI, Brabec CJ, Bernholc J. Nanomechanics of carbon tubes: instabilities beyond linear response. Phys. Rev. Lett., 1996; 76: 2511–2514.CrossRefGoogle Scholar
  4. 4.
    Srivastava D, Menon M, Cho K. Nanoplasticity of single-wall carbon nanotubes under uniaxial compression. Phys. Rev. Lett., 1999; 83: 2973–2976.CrossRefGoogle Scholar
  5. 5.
    Xiao T, Xu X, Liao K. Characterization of nonlinear elasticity and elastic instability in single-walled carbon nanotubes. J. Appl. Phys., 2004; 95: 8145–8148.CrossRefGoogle Scholar
  6. 6.
    Liew KM, Wong CH, He XQ, Tan MJ, Meguid SA. Nanomechanics of single and multiwalled carbon nanotubes. Phys. Rev. B., 2004; 69: 115429.CrossRefGoogle Scholar
  7. 7.
    Sears A, Batra RC. Macroscopic properties of carbon nanotubes from molecular-mechanics simulations. Phys. Rev. B, 2004; 69: 235406.CrossRefGoogle Scholar
  8. 8.
    Wang Y, Wang XX, Ni XG, Wu HA. Simulation of the elastic response and the buckling modes of single-walled carbon nanotubes. Comput Mater. Sci., 2005; 32: 141–146.CrossRefGoogle Scholar
  9. 9.
    Liew KM, Wong CH, Tan MJ. Tensile and compressive properties of carbon nanotube bundles. Acta Materialia, 2006; 54: 225–231.CrossRefGoogle Scholar
  10. 10.
    Liew KM, He XQ, Wong CH. On the study of elastic and plastic properties of multi-walled carbon nanotubes under axial tension using molecular dynamics simulation. Acta Materialia, 2004; 52: 2521–2527.CrossRefGoogle Scholar
  11. 11.
    Pantano A, Parks DM, Boyce MC. Mechanics of deformation of single-and multi-wall carbon nanotubes. J. Mech. Phys. Solids, 2004; 52: 789–821.zbMATHCrossRefGoogle Scholar
  12. 12.
    He XQ, Kitipornchai S, Liew KM. Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction. J. Mech. Phys. Solids, 2005; 53: 303–326.zbMATHCrossRefGoogle Scholar
  13. 13.
    Kitipornchai S, He XQ, Liew KM. Buckling analysis of triple-walled carbon nanotubes embedded in an elastic matrix. J. Appl. Phys., 2005; 97: 114318.CrossRefGoogle Scholar
  14. 14.
    Liu B, Huang Y, Jiang H, Qu S, Hwang KC. The atomic-scale finite element method. Comput Methods Appl. Mech. Engrg., 2004; 193: 1849–1864.zbMATHCrossRefGoogle Scholar
  15. 15.
    Liu B, Jiang H, Huang Y, Qu S, Yu MF, Hwang KC. Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes. Phys. Rev. B., 2005; 72: 035435.CrossRefGoogle Scholar
  16. 16.
    Brenner DW, Shenderova OA, Harrison JA, Stuart SJ, Ni B, Sinnott SB. A second-generation reactive empirical bond order (rebo) potential energy expression for hydrocarbons. J. Phys.: Condens. Matter, 2002; 14:783–802.CrossRefGoogle Scholar
  17. 17.
    Girifalco LA, Hodak M, Lee RS. Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential. Phys. Rev. B., 2000; 62: 13104–13110.CrossRefGoogle Scholar
  18. 18.
    ABAQUS. ABAQUS Theory Manual and Users Manual, version 6.2. Hibbit, Karlsson and Sorensen Inc., Pawtucket, RI, USA, 2002.Google Scholar
  19. 19.
    Menon M, Richter E, Subbaswamy KR. Structural and vibrational properties of fullerenes and nanotubes in a nonorthogonal tight-binding scheme. J. Chem. Phys., 1996; 104: 5875–5882.CrossRefGoogle Scholar
  20. 20.
    Humphrey W, Dalke A, Schulten K. VMD-visual molecular dynamics. J. Molec. Graphics, 1996; 14: 33–38.CrossRefGoogle Scholar
  21. 21.
    Timoshenko SP, Gere JM. Theory of Elastic Stability, 2-ed. McGraw-Hill, New York, USA, 1961.Google Scholar
  22. 22.
    Zhou X, Zhou JJ, Ouyang ZC. Strain energy and Young’s modulus of single-wall carbon nanotubes calculated from electronic energy-band theory. Phys. Rev. B., 2000; 62: 13692–13696.CrossRefGoogle Scholar
  23. 23.
    Kundin KN, Scuseria GE, Yakobson BI. C2F, BN, and C nanoshell elasticity from ab initio computations. Phys. Rev. B., 2001; 64: 235406.CrossRefGoogle Scholar
  24. 24.
    Tu ZC, Ouyang ZC. Single-walled and multiwalled carbon nanotubes viewed as elastic tubes with the effective Young’s moduli dependent on layer number. Physical Review B, 2002; 65(23): Art. No. 233407.Google Scholar
  25. 25.
    Yakobson BI, Brabec CJ, Bernholc J. Nanomechanics of carbon tubes: Instabilities beyond linear response. Physical Review Letters, 1996; 76(14): 2511–2514.CrossRefGoogle Scholar
  26. 26.
    Shibutani Y, Ogata S. Mechanical integrity of carbon nanotubes for bending and torsion. Modelling Simul Mater. Sci. Engrg, 2004; 12: 599–610.CrossRefGoogle Scholar
  27. 27.
    Wang Y, Wang XX, Ni XG. Atomistic simulation of the torsion deformation of carbon nanotubes. Modelling Simul. Mater. Sci. Engrg, 2004; 12: 1099–1107.CrossRefGoogle Scholar

Copyright information

© Tsinghua University Press & Springer 2007

Authors and Affiliations

  • A. Y. T. Leung
    • 1
  • Xiang Guo
    • 1
  1. 1.Department of Building and ConstructionCity University of Hong KongHong KongChina

Personalised recommendations