On a nanoscopically-informed shell theory of single-wall carbon nanotubes

European Journal of Mechanics, A/Solids

Volumn 42, Issue , 2013, Pages 137-157

  Bajaj, Chandrajit ^a   Favata, Antonino ^b   Podio Guidugli, Paolo ^c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b HAMBURG UNIVERSITY OF TECHNOLOGY   (Germany)

^c UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Shell theory; Single wall carbon nanotubes

Indexed keywords

SINGLE-WALLED CARBON NANOTUBES (SWCN);

EFFECTIVE RADIUS; EFFECTIVE THICKNESS; ELASTIC RESPONSE; MACROSCOPIC THEORY; SHELL THEORY; SINGLE-WALLED CARBON NANOTUBE (SWCNTS);

CHIRALITY;

EID: 84879973188     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2013.05.003     Document Type: Article

References (47)

1. X. Blanc, C. Le Bris, and P.L. Lions From molecular models to continuum mechanics Archive Ration. Mech. Anal. 164 4 2002 341 381 (Pubitemid 36185854)
2. G.X. Cao, and X. Chen The effects of chirality and boundary conditions on the mechanical properties of single-walled carbon nanotubes Int. J. Solids Struct. 44 2007 5447 5465 (Pubitemid 47048219)
3. T.C. Chang Torsional behavior of chiral singlewalled carbon nanotubes is loading direction dependent Appl. Phys. Lett. 90 2007 201910
4. T. Chang A molecular based anisotropic shell model for single-walled carbon nanotubes J. Mech. Pys. Sol. 58 9 2010 1422 1433
5. T. Chang, and H. Gao Size-dependent elastic properties of a single nanotube via a molecular model J. Mech. Phys. Solids 51 2003 1059
6. T. Chang, J. Geng, and X. Guo Chirality- and size-dependent elastic properties of single-walled carbon nanotubes Appl. Phys. Lett. 87 2005 251929
7. T. Chang, J. Geng, and X. Guo Prediction of chirality-and size-dependent elastic properties of single-walled carbon nanotubes via a molecular mechanics model Proc. R. Soc. A 462 2006 2523 2540 (Pubitemid 44922061)
8. C. Davini Homogeneization of a graphene sheet Cont. Mech. Therm. 2013 10.1007/s00161-013-0292-y
9. A. Favata, and P. Podio-Guidugli A new CNT-oriented shell theory Eur. J. Mech. A/Sol. 35 2012 75 96
10. A. Favata, and P. Podio-Guidugli A Shell Theory for Chiral Single-wall Carbon Nanotubes 2012 (submitted for publication)
11. J. Geng, and T. Chang Nonlinear stick-spiral model for predicting mechanical behavior of single-walled carbon nanotubes Phys. Rev. B 74 2006 245428
12. S.K. Georgantzinos, G.I. Giannopoulos, and N.K. Anifantis Numerical investigation of elastic mechanical properties of graphene structures Mater. Des. 31 10 2010 4646 4654
13. S.K. Georgantzinos, G.I. Giannopoulos, D.E. Katsareas, P.A. Kakavas, and N.K. Anifantis Size-dependent non-linear mechanical properties of graphene nanoribbons Comput. Mat. Sci. 50 7 2011 20572062
14. G.I. Giannopoulos Elastic buckling and flexural rigidity of graphene nanoribbons by using a unique translational spring element per interatomic interaction Comput. Mat. Sci. 53 1 2012 388395
15. G.I. Giannopoulos, I.A. Liosatos, and A.K. Moukanidis Parametric study of elastic mechanical properties of graphene nanoribbons by a new structural mechanics approach Physica E 44 1 2011 124 134
16. R.V. Goldstein, V.A. Gorodtsov, A.V. Chentsov, S.V. Starikov, V.V. Stegailov, and G.E. Norman To Description of Mechanical Properties of Nanotubes Tube Wall Thickness Problem. Size Effect 2010 Russian Academy of Sciences, A.Yu. Ishlinsky Institute for Problems in Mechanics Preprint 937
17. R.V. Goldstein, V.A. Gorodtsov, and D.S. Lisovenko To the description of multilayer nanotubes in models of cylindrically anisotropic elasticity Phys. Mesomech. 13 2010 1 2
18. M.E. Gurtin The Linear Theory of Elasticity Handbuch der Physik vol. VIa/2 1972 Springer 1 295
19. E. Hernandez, C. Goze, P. Bernier, and A. Rubio Elastic Properties of C and BxCyNz composite nanotubes Phys. Rev. Lett. 80 1998 4502
20. Y. Huang, J. Wu, and K.C. Hwang Thickness of graphene and single-wall carbon nanotubes Phys. Rev. B 74 2006 245413
21. S. Iijima Helical microtubules of graphitic carbon Nature 354 1991 56 58 (Pubitemid 21896780)
22. Y. Jin, and F.G. Yuan Simulation of elastic properties of single-walled carbon nanotubes Compos. Sci. Technol. 63 2003 1507 1515 (Pubitemid 36906665)
23. K.N. Kudin, G.E. Scuseria, and B.I. Yakobson C2F, BN and C nano-shell elasticity by ab initio computations Phys. Rev. B 64 2001 235406 235410
24. C. Le Bris, and P.L. Lions From atoms to crystals: a mathematical journey Bull. Am. Math. Soc. 42 291 2005 363
25. C. Li, and T.-W. Chou A structural mechanics approach for the analysis of carbon nanotubes Int. J. Solids Struct. 40 2003 2487
26. J.P. Lu Elastic properties of carbon nanotubes and nanoropes Phys. Rev. Lett. 79 1997 1297
27. P.G. Martinsson, and I. Babuška Mechanics of materials with periodic truss or frame micro-structures Arch. Rational Mech. Anal. 185 2007 201 234
28. G.M. Odegard Modeling of carbon nanotube/polymer composites M.J. Schulz, A. Kelkar, M.J. Sundaresan, Nanoengineering of Structural, Functional and Smart Materials 2005 CRC Press
29. G.M. Odegard Equivalent-continuum modeling of nanostructured materials M. Rieth, W. Schommers, Handbook of Theoretical and Computational Nanotechnology 2006 American Scientific Publishers
30. A. Pantano, D.M. Parks, and M.C. Boyce Mechanics of deformation of single- and multi-wall carbon nanotubes J. Mech. Phys. Solids 52 4 2004 789 821
31. P. Podio-Guidugli On structure thinness, mechanical and variational E. Taroco, E.A. de Souza Neto, A.A. Novotny, Variational Formulations in Mechanics: Theory and Applications 2007 CIMNE 227 242
32. N. Pugno New quantized failure criteria: application to nanotubes and nanowires Int. J. Fract. 141 2006 311 323
33. N. Pugno, F. Marino, and A. Carpinteri Towards a periodic table for nano-mechanical properties of elements Int. J. Solids Struct. 43 2006 5647 5657 (Pubitemid 44067015)
34. A. Raoult, D. Caillerie, and A. Mourad Elastic lattices: equilibrium, invariant laws and homogenization Ann. Univ. Ferrara 54 2 2008 297 318
35. C.Q. Ru Chirality-dependent mechanical behavior of carbon nanotubes based on an anisotropic elastic shell model Math. Mech. Sol 14 2009 88 101
36. L. Shen, and J. Li Transversely isotropic properties of single-walled carbon nanotube Phys. Rev. B 69 2004 045414
37. O.A. Shenderova, V.V. Zhirnov, and D.W. Brenner Carbon nanostructures Crit. Rev. Solid State Mater. Sci. 27 2002 227 356
38. Z.C. Tu, and Z.C. Ou-Yang Single-walled and multiwalled carbon nanotubes viewed as elastic tubes with the effective Young's moduli dependent on layer number Phys. Rev. B 65 2002 233407
39. T. Vodenitcharova, and L.C. Zhang Effective wall thickness of a single-walled carbon nanotube Phys. Rev. B 68 2003 165401
40. H. Wan, and F. Delale A structural mechanics approach for predicting the mechanical properties of carbon nanotubes Meccanica 45 2010 4351
41. Q. Wang Effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes Int. J. Solids Struct. 41 2004 5451 5461
42. L. Wang, Q. Zheng, J.Z. Liu, and Q. Jiang Size dependence of the thin-shell model for carbon nanotubes Phys. Rev. Lett. 95 2005 8297
43. J. Wu, K.C. Hwang, and Y. Huang An atomistic-based finite-deformation shell theory for single-wall carbon nanotubes J. Mech. Phys. Solids 54 2008 279 292
44. J. Xiao, B. Gama, and J. Gillespie Jr. An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes Int. J. Solids Struct. 42 2005 3075 3092 (Pubitemid 40200619)
45. B.I. Yakobson, C.J. Brabec, and J. Bernholc Nanomechanics of carbon tubes: instabilities beyond linear regime Phys. Rev. Lett. 76 1996 2511
46. Y.Y. Zhang, V.B. Tan, and C.M. Wang Effect of chirality on buckling behavior of singlewalled carbon nanotubes J. Appl. Phys. 100 2006 074304
47. X. Zhou, J.J. Zhou, and Z.C. Ou-yang Strain energy and Young's modulus of single-wall carbon nanotubes calculated from electronic energy-band theory Phys. Rev. B 62 2000 13692