Buckling and postbuckling analysis of multi-walled carbon nanotubes based on the continuum shell model

International Journal of Structural Stability and Dynamics

Volumn 7, Issue 4, 2007, Pages 629-645

  He, X Q ^a   Qu, C ^b   Qin, Q H ^c   Wang, C M ^d  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b TIANJIN UNIVERSITY   (China)

^c AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^d NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Carbon nanotubes; Classical thin shell theory; Continuum model; Postbuckling; Van der Waals force

Indexed keywords

MATHEMATICAL MODELS; MULTIWALLED CARBON NANOTUBES (MWCN); NONLINEAR ANALYSIS; VAN DER WAALS FORCES;

CLASSICAL THIN SHELL THEORY; CONTINUUM MODEL; POSTBUCKLING;

BUCKLING;

EID: 36549071067     PISSN: 02194554     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219455407002460     Document Type: Article

References (39)

1. P. Ball, Roll up for the revolution, Nature 414 (2001) 142-144.
2. R. H. Baughman, A. A. Zakhidov and W. A. de Heer, Carbon nanotubes -The route toward applications, Science 297 (2002) 787-792.
3. S. Iijima, Helical microtubes of graphitic carbon, Nature 354 (1991) 56-58.
4. S. Iijima, C. Brabec, A. Maiti and J. Bernholc, Structural flexibility of carbon nanotubes, J. Chem. Phys. 104 (1996) 2089-2092.
5. B. I. Yakobson, C. J. Brabec and J. Bernholc, Nanomechanics of carbon tubes: Instabilities beyond linear response, Phys. Rev. Lett. 76 (1996) 2511-2514.
6. B. Ni, S. B. Sinnott, P. T. Mikulski and J. A. Harrison, Compression of carbon nanotubes filled with C 60, CH4, or Ne: Predictions from molecular dynamics simulations, Phys. Rev. Lett. 88 (2002) 205505.
7. M. M. J. Treacy, T. W. Ebbesen and J. M. Gibson, Exceptionally high Young's modulus observed for individual carbon nanotubes, Nature 381 (1996) 678-680.
8. E. W. Wong, P. E. Sheehan and C. M. Lieber, Nanobeam mechanics: Elasticity, strength, and toughness of nanorods and nanotubes, Science 277 (1997) 1971-1975.
9. S. Govindjee and J. L. Sackman, On the use of continuum mechanics to estimate the properties of nanotubes, Solid State Commun. 110 (1999) 227-230.
10. C. M. Wang, V. B. C. Tan and Y. Y. Zhang, Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes, J. Sound Vib. 294 (2006) 1060-1072.
11. C. Li and T. W. Chou, A structural mechanics approach for the analysis of carbon nanotubes, Int. J. Solids Struct. 40 (2003) 2487-2499.
12. G. M. Odegard, T. S. Gates, L. M. Nicholson and K. E. Wise, Equivalent-continuum modeling of nano-structured materials, Compos. Sci. Technol. 62 (2002) 1869-1880.
13. A. Pantano, M. C. Boyce and D. M. Parks, Nonlinear structural mechanics based modeling of carbon nanotube deformation, Phys. Rev. Lett. 91 (2003) 145504.
14. A. Pantano, D. M. Parks and M. C. Boyce, Mechanics of deformation of single- and multi-wall carbon nanotubes, J. Mech. Phys. Solids 52 (2004) 789-821.
15. M. R. Falvo, G. J. Clary, R. M. Taylor, V. Chi, F. P. Brooks, S. Washburn and R. Superfine, Bending and buckling of carbon nanotubes under large strain, Nature 389 (1997) 582-584.
16. C. Q. Ru, Effective bending stiffness of carbon nanotubes, Phys. Rev. B 62 (2000) 9973-9976.
17. C. Q. Ru, Axially compressed buckling of a double-walled carbon nanotube embedded in an elastic medium, J. Mech. Phys. Solids 49 (2001) 1265-1279.
18. R. S. Ruoff, J. Tersoff, D. C. Lorents, S. Subramoney and B. Chan, Radial deformation of carbon nanotubes by van der Waals forces, Nature 364 (1993) 514-516.
19. J. Tersoff and R. S. Ruoff, Structural properties of a carbon-nanotube crystal, Phys. Rev. Lett. 73 (1994) 676-679.
20. J. Lu, Elastic properties of carbon nanotubes and nanoropes, Phys. Rev. Lett. 79 (1997) 1297-1300.
21. T. Hertel, R. E. Walkup and P. Avouris, Deformation of carbon nanotubes by surface van der Waals forces, Phys. Rev. B 58 (1998) 13870-13873.
22. H. S. Shen, Postbuckling prediction of double-walled carbon nanotubes under hydrostatic pressure, Int. J. Solids. Struct. 41 (2003) 2643-2657.
23. X. Q. He, S. Kitipornchai and K. M. Liew, Buckling analysis of multi-walled carbon nanotubes: A continuum model accounting for vdW interaction, J. Mech. Phys. Solids 53 (2005) 303-326.
24. H. S. Shen and C. L. Zhang, Postbuckling prediction of axially loaded double-walled carbon nanotubes with temperature dependent properties and initial defects, Phys. Rev. B 74 (2006) 035410.
25. H. S. Shen and C. L. Zhang, Postbuckling of double-walled carbon nanotubes with temperature dependent properties and initial defects under combined axial and radial mechanical loads, Int. J. Solids Struct. 44 (2007) 1461-1487.
26. C. L. Zhang and H. S. Shen, Buckling and postbuckling analysis of single-walled carbon nanotubes in thermal environments via molecular dynamics simulation, Carbon 44 (2006) 2608-2616.
27. C. L. Zhang and H. S. Shen, Temperature-dependent elastic properties of single-walled carbon nanotubes: Prediction from molecular dynamics simulation, Appl. Phys. Lett. 89 (2006) 081904.
28. Q. Wang, Wave propagation in carbon nanotubes via, nonlocal continuum mechanics, J. Appl. Phys. 98 (2005) 124301.
29. Q. Wang and C. M. Wang, The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes, Nanotechnology 18 (2007) 075702.
30. Y. Q. Zhang, G. R. Liu and J. S. Wang, Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression, Phys. Rev. B 70 (2004) 205430.
31. L. F. Wang and H. Y. Hu, Flexural wave propagation in single-walled carbon nanotubes, Phys. Rev. B 71 (2005) 195412.
32. C. M. Wang, Y. Y. Zhang and X. Q. He, Vibration of nonlocal Timoshenko beams, Nanotechnology 18 (2007) 105401.
33. C. M. Wang, Y. Y. Zhang, S. S. Ramesh and S. Kitipornchai, Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory, J. Phys. D, Appl. Phys. 39 (2006) 3904-3909.
34. J. Chen and C. D. Babcock, Nonlinear vibration of cylindrical shells, AIAA J. 13 (1975) 868-876.
35. R. Saito, R. Matsuo, T. Kimura, G. Dresselhaus and M. S. Dresselhaus, Anomalous potential barrier of double-wall carbon nanotube, Chem. Phys. Lett. 348 (2001) 187-193.
36. N. N. Bogoliubov and Y. A. Mitropolsky, Asymptotic Methods in the Theory of Non-Linear Oscillations (Gordon & Breach Sci. Publishing, 1961).
37. D. A. Evensen, A Theoretical and Experimental Study of the Nonlinear Flexural Vibrations of Thin Circular Rings, NASA TR, R-227 (1965).
38. K. M. Liew, C. H. Wong, X. Q. He, M. J. Tan and S. A. Meguid, Nanomechanics of single and multiwalled carbon nanotubes, Phys. Rev. B 69 (2004) 115429.
39. S. P. Timoshenko and J. M. Gere, Mechanics of Materials (Van Nostrand Reinhold Company, USA, 1973).