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A structural mechanics approach for predicting the mechanical properties of carbon nanotubes

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Abstract

Based on molecular mechanics, a structural mechanics model of carbon nanotubes (CNTs) was developed with special consideration given to the bending stiffness of the graphite layer. The potentials associated with the atomic interactions within a CNT were evaluated by the strain energies of beam elements which serve as structural substitutions of covalent bonds in a CNT. In contrast to the original model developed by Li and Chou (Int. J. Solids Struct. 40(10):2487–2499, 2003), in the current model the out-of-plane deformation (inversion) of the bond was distinguished from the in-plane deformation by considering a rectangular cross-section for the beam element. Consequently, the model is able to study problems where the effect of local bending of the graphite layer in a carbon nanotube is significant. A closed-form solution of the sectional properties of the beam element was derived analytically. The model was verified through the analysis of rolling a graphite sheet into a carbon nanotube. Using the present model, the buckling behavior of nanotubes under bending is simulated. The predicted critical bending angle agrees well with molecular dynamics simulations.

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References

  1. Li C, Chou T-W (2003) A structural mechanics approach for the analysis of carbon nanotubes. Int J Solids Struct 40(10):2487–2499

    Article  MATH  Google Scholar 

  2. Harik VM (2001) Ranges of applicability for the continuum beam model in the mechanics of carbon nanotubes and nanorods. Solid State Commun 120:331–335

    Article  ADS  Google Scholar 

  3. Yakobson BI, Brabec CJ, Bernholc J (1996) Nanomechanics of carbon tubes: Instabilities beyond linear response. Phys Rev Lett 76(14):2511

    Article  ADS  Google Scholar 

  4. Ru CQ (2000) Effective bending stiffness of carbon nanotubes. Phys Rev B 62(15):9973

    Article  ADS  Google Scholar 

  5. Shen L, Li J (2005) Equilibrium structure and strain energy of single-walled carbon nanotubes. Phys Rev B (Condens Matter Mater Phys) 71(16):165427-8

    ADS  Google Scholar 

  6. Chang T, Gao H (2003) Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model. J Mech Phys Solids 51:1059–1074

    Article  MATH  ADS  Google Scholar 

  7. Shen L, Li J (2004) Transversely isotropic elastic properties of single-walled carbon nanotubes. Phys Rev B (Condens Matter Mater Phys) 69(4):045414-10

    ADS  Google Scholar 

  8. Odegard GM, Gates TS, Nicholson LM, Wise KE (2002) Equivalent-continuum modeling of nano-structured materials. Compos Sci Technol 62:1869–1880

    Article  Google Scholar 

  9. Huang M-Y, Chen H-B, Lu J-N, Lu P, Zhang P-Q (2006) A modified molecular structural mechanics method for analysis of carbon nanotubes. Chinese J Chem Phys 19(4):286–290

    Google Scholar 

  10. Li C, Chou T-W (2004) Modeling of elastic buckling of carbon nanotubes by molecular structural mechanics approach. Mech Mater 36:1047–1055

    Article  Google Scholar 

  11. Li C, Chou T-W (2005) Modeling of carbon nanotube clamping in tensile tests. Compos Sci Technol 65:2407–2415

    Article  Google Scholar 

  12. Tu Z-C, Ou-Yang Z-C (2002) Single-walled and multiwalled carbon nanotubes viewed as elastic tubes with the effective Young’s moduli dependent on layer number. Phys Rev B 65:233407

    Article  ADS  Google Scholar 

  13. Kundin KN, Scuseria GE, Yakobson BI (2001) C2f, bn, and c nanoshell elasticity from ab initio computations. Phys Rev B 64:235406

    ADS  Google Scholar 

  14. Pantano A, Parks DM, Boyce MC (2004) Mechanics of deformation of single- and multi-wall carbon nanotubes. J Mech Phys Solids 52(4):789–821

    Article  MATH  ADS  Google Scholar 

  15. Zhou X, Zhou JJ, Ou-Yang ZC (2000) Strain energy and Young’s modulus of single-wall carbon nanotubes calculated from electronic energy-band theory. Phys Rev B 62(20):13692–13696

    Article  ADS  Google Scholar 

  16. Robertson DH, Brenner DW, Mintmire JW (1992) Energetics of nanoscale graphitic tubules. Phys Rev B 45(21):12592

    Article  ADS  Google Scholar 

  17. Miyamoto Y, Rubio A, Louie SG, Cohen ML (1994) Electronic properties of tubule forms of hexagonal bc_{3}. Phys Rev B 50(24):18360

    Article  ADS  Google Scholar 

  18. Kurti J, Kresse G, Kuzmany H (1998) First-principles calculations of the radial breathing mode of single-wall carbon nanotubes. Phys Rev B 58(14):R8869

    Article  ADS  Google Scholar 

  19. Sanchez-Portal D, Artacho E, Soler JM, Rubio A, Ordejon P (1999) Ab initio structural, elastic, and vibrational properties of carbon nanotubes. Phys Rev B 59(19):12678

    Article  ADS  Google Scholar 

  20. Hernandez E, Goze C, Bernier P, Rubio A (1998) Elastic properties of c and b x c y n z composite nanotubes. Phys Rev Lett 80(20):4502

    Article  ADS  Google Scholar 

  21. Mylvaganam K, Vodenitcharova T, Zhang LC (2006) The bending-kinking analysis of a single-walled carbon nanotube—a combined molecular dynamics and continuum mechanics technique. J Mater Sci 41:3341–3347

    Article  ADS  Google Scholar 

  22. Tu ZC, Ou-Yang ZC (2008) Elastic theory of low-dimensional continua and its applications in bio- and nano-structures. J Comput Theor Nanosci 5:422–448

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, The City College of New York, 138th Street and Convent Avenue, New York, NY, 10031, USA

    H. Wan & F. Delale

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  1. H. Wan
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  2. F. Delale
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Correspondence to F. Delale.

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Wan, H., Delale, F. A structural mechanics approach for predicting the mechanical properties of carbon nanotubes. Meccanica 45, 43–51 (2010). https://doi.org/10.1007/s11012-009-9222-2

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  • DOI: https://doi.org/10.1007/s11012-009-9222-2

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