A nonlinear van der Waals force model for multiwalled carbon nanotubes modeled by a nested system of cylindrical shells

Journal of Applied Mechanics, Transactions ASME

Volumn 77, Issue 6, 2010, Pages

  He, X Q ^a   Kitipornchai, S ^a   Wang, C M ^b   Xiang, Y ^c   Zhou, Q ^d  

^a CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c UNIVERSITY OF WESTERN SYDNEY   (Australia)

^d WUHAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BUCKLING LOADS; BUCKLING RESPONSE; BUCKLING STRAIN; COMMONLY USED; CYLINDRICAL SHELL; CYLINDRICAL SHELL MODEL; FORCE MODEL; NONLINEAR TERMS; POSTBUCKLING ANALYSIS; POSTBUCKLING RESPONSE; TAYLOR EXPANSIONS; VAN DER WAALS INTERACTION;

BUCKLING; CARBON NANOTUBES; COMPUTER SIMULATION; MULTIWALLED CARBON NANOTUBES (MWCN); SHELLS (STRUCTURES);

VAN DER WAALS FORCES;

EID: 78649995117     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.4001859     Document Type: Article

References (44)

1. Tadmor, E. B., Smith, G. S., Bernstein, N., and Kaxiras, E., 1999, "Mixed Finite Element and Atomistic Formulation for Complex Crystals, " Phys. Rev. B, 59, pp. 235-245.
2. Zhang, P., Huang, Y., Geubelle, P. H., Klein, P. A., and Hwang, K. C., 2002, "The Elastic Modulus of Single-Wall Carbon Nanotubes: A Continuum Analysis Incorporating Interatomic Potentials, " Int. J. Solids Struct., 39, pp. 3893-3906.
3. Zhang, P., Jiang, H., Huang, Y., Geubelle, P. H., and Hwang, K. C., 2004, "An Atomistic-Based Continuum Theory for Carbon Nanotubes: Analysis of Fracture Nucleation, " J. Mech. Phys. Solids, 52, pp. 977-998.
4. Brenner, D. W., 1990, "Empirical Potential for Hydrocarbons for use in Simulating the Chemical Vapour Deposition of Diamond Films, " Phys. Rev. B, 42, pp. 9458-9471.
5. Arroyo, M., and Belytschko, T., 2002, "An Atomistic-Based Finite Deformation Membrane for Single Layer Crystalline Films, " J. Mech. Phys. Solids, 50, pp. 1941-1977.
6. Arroyo, M., and Belytschko, T., 2004, "Finite Element Methods for the Non-Linear Mechanics of Crystalline Sheets and Nanotubes, " Int. J. Numer. Methods Eng., 59, pp. 419-456.
7. Jiang, H., Zhang, P., Liu, B., Huang, Y., Geubelle, P. H., Gao, H., and Hwang, K. C., 2003, "The Effect of Nanotube Radius on the Constitutive Model for Carbon Nanotubes, " Comput. Mater. Sci., 28, pp. 429-442.
8. Wu, J., Hwang, K. C., and Huang, Y., 2008, "An Atomistic-Based Finite-Deformation Shell Theory for Single-Wall Carbon Nanotubes, " J. Mech. Phys. Solids, 56, pp. 279-292.
9. Sunyk, R., and Steinmann, P., 2003, "On Higher Gradients in Continuum-Atomistic Modeling, " Int. J. Solids Struct., 40, pp. 6877-6896.
10. Guo, X., Wang, J. B., and Zhang, H. W., 2006, "Mechanical Properties of Single-Walled Carbon Nanotubes Based on Higher Order Cauchy-Born Rule, " Int. J. Solids Struct., 43, pp. 1276-1290.
11. Wang, J. B., Guo, X., Zhang, H. W., Wang, L., and Liao, J. B., 2006, "Energy and Mechanical Properties of Single-Walled Carbon Nanotubes Predicted Using the Higher Order Cauchy-Born Rule, " Phys. Rev. B, 73, p. 115428.
12. Sun, Y. Z., and Liew, K. M., 2008, "The Buckling of Single-Walled Carbon Nanotubes Upon Bending: The Higher Order Gradient Continuum and Mesh-Free Method, " Comput. Methods Appl. Mech. Eng., 197, pp. 3001-3013.
13. Liew, K. M., and Sun, Y. Z., 2008, "Elastic Properties and Pressure-Induced Structural Transitions of Single-Walled Carbon Nanotubes, " Phys. Rev. B, 77, p. 205437.
14. Qian, D., Wagner, G. J., Ruoff, R. S., Yu, M. F., and Liu, W. K., 2002, "Mechanics of Carbon Nanotubes, " Appl. Mech. Rev., 55, pp. 495-533.
15. Huang, Y., and Wang, Z. L., 2003, Comprehensive Structural Integrity Handbook 8, Elsevier, New York, pp. 551-579.
16. Yakobson, B. I., Brabec, C. J., and Bernholc, J., 1996, "Nanomechanics of Carbon Tubes: Instabilities Beyond Linear Response, " Phys. Rev. Lett., 76, pp. 2511-2514.
17. Ru, C. Q., 2001, "Axially Compressed Buckling of a Double-Walled Carbon Nanotube Embedded in an Elastic Medium, " J. Mech. Phys. Solids, 49, pp. 1265-1279.
18. Wang, Q., Duan, W. H., Liew, K. M., and He, X. Q., 2007, "Inelastic Buckling of Carbon Nanotubes, " Appl. Phys. Lett., 90, p. 033110.
19. Zhang, Y. Y., Wang, C. M., and Tan, V. B. C., 2006, "Buckling of Multi-Walled Carbon Nanotubes Using Timoshenko Column Model, " J. Eng. Mech., 132, pp. 952-958.
20. Popov, V. N., and Henrard, L., 2002, "Breathinglike Phonon Modes of Multiwalled Carbon Nanotubes, " Phys. Rev. B, 65, p. 235415.
21. Wang, C. M., Zhang, Y. Y., and He, X. Q., 2007, "Vibration of Nonlocal Timoshenko Beams, " Nanotechnology, 18, p. 105401.
22. He, X. Q., Eisenberger, M., and Liew, K. M., 2006, "The Effect of Van der Waals Interaction Modeling on the Vibration Characteristics of Multiwalled Carbon Nanotubes, " J. Appl. Phys., 100, p. 124317.
23. Wang, C. Y., Ru, C. Q., and Miduchowski, A., 2004, "Applicability and Limitations of Simplified Elastic Shell Equations for Carbon Nanotubes, " ASME J. Appl. Mech., 71, pp. 622-631.
24. Natsuki, T., Hayashi, T., and Endo, M., 2005, "Wave Propagation of Carbon Nanotubes Embedded in an Elastic Medium, " J. Appl. Phys., 97, p. 044307.
25. Li, C. Y., and Chou, T. W., 2003, "Single-Walled Carbon Nanotubes as Ultrahigh Frequency Nanomechanical Resonators, " Phys. Rev. B, 68, p. 073405.
26. Yoon, J., Ru, C. Q., and Mioduchowski, A., 2002, "Noncoaxial Resonance of an Isolated Multiwall Carbon Nanotube, " Phys. Rev. B, 66, p. 233402.
27. Falvo, M. R., Clary, G. J., Taylor, R. M., Chi, V., Brooks, F. P., Washburn, S., and Superfine, R., 1997, "Bending and Buckling of Carbon Nanotubes Under Large Strain, " Nature (London), 389, pp. 582-584.
28. Wang, Q., 2004, "Effective In-Plane Stiffness and Bending Rigidity of Armchair and Zigzag Carbon Nanotubes, " Int. J. Solids Struct., 41, pp. 5451-5461.
29. Natsuki, T., Endo, M., and Tsuda, H., 2006, "Vibration Analysis of Embedded Carbon Nanotubes Using Wave Propagation Approach, " J. Appl. Phys., 99, p. 034311.
30. Wang, L. F., and Hu, H. Y., 2005, "Transverse Wave Propagation in Single-Walled Carbon Nanotubes, " Phys. Rev. B, 71, p. 195412.
31. He, X. Q., Kitipornchai, S., and Liew, K. M., 2005, "Buckling Analysis of Multi-Walled Carbon Nanotubes: A Continuum Model Accounting for Van der Waals Interaction, " J. Mech. Phys. Solids, 53, pp. 303-326.
32. Kitipornchai, S., He, X. Q., and Liew, K. M., 2005, "Buckling Analysis of Triple-Walled Carbon Nanotubes Embedded in an Elastic Matrix, " J. Appl. Phys., 97, p. 114318.
33. Chang, T. C., Guo, W. L., and Guo, X. M., 2005, "Buckling of Multiwalled Carbon Nanotubes Under Axial Compression and Bending via a Molecular Mechanics Model, " Phys. Rev. B, 72, p. 064101.
34. Lu, W. B., Liu, B., Wu, J., Xiao, J., Hwang, K. C., Fu, S. Y., and Huang, Y., 2009, "Continuum Modeling of Van der Waals Interactions Between Carbon Nanotube Walls, " Appl. Phys. Lett., 94, p. 101917.
35. Xu, K. Y., Guo, X. N., and Ru, C. Q., 2006, "Vibration of a Double-Walled Carbon Nanotube Aroused by Nonlinear Intertube Van der Waals Forces, " J. Appl. Phys., 99, p. 064303.
36. Shen, H. S., 2004, "Postbuckling Prediction of Double-Walled Nanotubes Under Hydrostatic Pressure, " Int. J. Solids Struct., 41, pp. 2643-2657.
37. Shen, H. S., and Zhang, C. L., 2006, "Postbuckling Prediction of Axially Loaded Double-Walled Carbon Nanotubes With Temperature Dependent Properties and Initial Defects, " Phys. Rev. B, 74, p. 035410.
38. Shen, H. S., and Zhang, C. L., 2007, "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, pp. 1461-1487.
39. Lennard-Jones, J. E., 1924, "The Determination of Molecular Fields. I. From the Variation of the Viscosity of a Gas With Temperature, " Proc. R. Soc. London A, 106, pp. 441-462.
40. Girifalco, L. A., and Lad, R. A., 1956, "Energy of Cohesion, Compressibility, and the Potential Energy Function of Graphite System, " J. Chem. Phys., 25, pp. 693-697.
41. Chen, J., and Babcock, C. D., 1975, "Nonlinear Vibration of Cylindrical Shells, " AIAA J., 13, pp. 868-876.
42. He, X. Q., Qu, C., and Qin, Q. H., 2007, "Buckling and Post-Buckling Analysis of Multi-Walled Carbon Nanotubes Based on the Continuum Shell Model, " Int. J. Struct. Stab. Dyn., 7, pp. 629-645.
43. Liew, K. M., Wong, C. H., He, X. Q., Tan, M. J., and Meguid, S. A., 2004, "Nanomechanics of Single and Multiwalled Carbon Nanotubes, " Phys. Rev. B, 69, pp. 115429.
44. Allen, H. G., and Bulson, P. S., 1980, Background To Buckling, McGraw-Hill, UK.