Abstract
Computational modelling of the mechanical characteristics of carbon nanotubes forms one of the most intensively studied topics in the nanomechanics field. The underlying motivation for this interest is evident. Carbon nanotubes, due to their unique and exotic mechanical properties, play a pivotal role in nanoscience and in all fields of nanotechnology, and in materials science and technology. A thorough understanding of their mechanical characteristics, including their static deformation properties, their buckling and vibrational behaviour, is therefore crucial for the design and construction of nanodevices. Owing to the extensive research output pertinent to the use of the nonlocal approach in modelling the mechanics of carbon nanotubes, we have divided the material in this chapter into two subsections; with the first subsection providing the mechanical characteristics of large aspect ratio SWCNTs, which are modelled using the nonlocal beam theories, while in the second subsection, we employ the nonlocal shell models to theoretically study the mechanical behaviour of carbon nanotubes. In the present chapter, we use the nonlocal differential approach owing to its wide and successful use in solving various mechanical problems related to carbon nanotubes. Some challenges facing the applications of the nonlocal differential approach to carbon nanotubes will be discussed in Chap. 12.
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References
V.M. Harik, Mechanics of carbon nanotubes: applicability of the continuum-beam models. Comput. Mater. Sci. 24, 328–342 (2002)
H. Rafii-Tabar, Computational Physics of Carbon Nanotubes (Cambridge University Press, Cambridge, 2008)
L.J. Sudak, Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics. J. Appl. Phys. 94, 7281–7287 (2003)
J. Peddieson, G.R. Buchanan, R.P. McNitt, Application of nonlocal continuum models to nanotechnology. Int. J. Eng. Sci. 41, 305–312 (2003)
Q. Wang, V.K. Varadan, S.T. Quek, Small scale effect on elastic buckling of carbon nanotubes with nonlocal continuum models. Phys. Lett. A 357, 130–135 (2006)
Q. Wang, K.M. Liew, Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures. Phys. Lett. A 363, 236–242 (2007)
P. Lu, H.P. Lee, C. Lu, P.Q. Zhang, Application of nonlocal beam models for carbon nanotubes. Int. J. Solids Struct. 44, 5289–5300 (2007)
J.N. Reddy, Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci. 45, 288–307 (2007)
M. Aydogdu, A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration. Phys. E 41, 1651–1655 (2009)
R. Barretta, F.M. de Sciarra, A nonlocal model for carbon nanotubes under axial loads. Adv. Mater. Sci. Eng. 2013, 360935 (2013)
B. Arash, Q. Wang, A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comput. Mater. Sci. 51, 303–313 (2012)
H. Rafii-Tabar, E. Ghavanloo, S.A. Fazelzadeh, Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures. Phys. Rep. 638, 1–97 (2016)
M.A. Eltaher, M.E. Khater, S.A. Emam, A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl. Math. Model. 40, 4109–4128 (2016)
H. Askari, D. Younesian, E. Esmailzadeh, L. Cveticanin, Nonlocal effect in carbon nanotube resonators: a comprehensive review. Adv. Mech. Eng. 9, 1–24 (2017)
L. Behera, S. Chakraverty, Recent researches on nonlocal elasticity theory in the vibration of carbon nanotubes using beam models: a review. Arch. Comput. Methods Eng. 24, 481–494 (2017)
S. Gopalakrishnan, S. Narendar, Wave Propagation in Nanostructures: Nonlocal Continuum Mechanics Formulations (Springer, Switzerland, 2013)
D. Karlicic, T. Murmu, S. Adhikari, M. McCarthy, Nonlocal Structural Mechanics (Wiley-ISTE, London, 2016)
C.M. Wang, Y.Y. Zhang, X.Q. He, Vibration of nonlocal Timoshenko beams. Nanotechnology 18, 105401 (2007)
N. Khosravian, H. Rafii-Tabar, Computational modelling of a non-viscous fluid flow in a multi-walled carbon nanotube modelled as a Timoshenko beam. Nanotechnology 19, 275703 (2008)
A. Benzair, A. Tounsi, A. Besseghier, H. Heireche, N. Moulay, L. Boumia, The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. J. Phys. D Appl. Phys. 41, 225404–225413 (2008)
E. Ghavanloo, S.A. Fazelzadeh, Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid. Phys. E 44, 17–24 (2011)
B. Motevalli, A. Montazeri, J.Z. Liu, H. Rafii-Tabar, Comparison of continuum-based and atomistic-based modeling of axial buckling of carbon nanotubes subject to hydrostatic pressure. Comput. Mater. Sci. 79, 619–626 (2013)
R. Merli, C. Lázaro, S. Monleón, A. Domingo, A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: new general formulation. Comput. Struct. 127, 68–87 (2013)
C.M. Wang, C.Y. Wang, J.N. Reddy, Exact Solutions for Buckling of Structural Members (CRC Press, Florida, 2005)
M.A. Maneshi, E. Ghavanloo, S.A. Fazelzadeh, Closed-form expression for geometrically nonlinear large deformation of nano-beams subjected to end force. Eur. Phys. J. Plus 133, 256 (2018)
C.Q. Ru, Elastic models for carbon nanotubes, in Encyclopaedia of Nanoscience and Nanotechnology, vol. 2, ed. by H.S. Nalwa (American Scientific, Stevenson Ranch, 2004), pp. 731–744
M. Shaban, A. Alibeigloo, Three dimensional vibration and bending analysis of carbon nanotubes embedded in elastic medium based on theory of elasticity. Lat. Am. J. Solids Struct. 11, 2122–2140 (2014)
X.Q. He, C. Qu, Q.H. Qin, C.M. Wang, Buckling and postbuckling analysis of multi-walled carbon nanotubes based on the continuum shell model. Int. J. Struct. Stab. Dyn. 7, 629–645 (2007)
N. Silvestre, C.M. Wang, Y.Y. Zhang, Y. Xiang, Sanders shell model for buckling of single-walled carbon nanotubes with small aspect ratio. Compos. Struct. 93, 1683–1691 (2011)
C.Y. Wang, L.C. Zhang, An elastic shell model for characterizing single-walled carbon nanotubes. Nanotechnology 19, 195704 (2008)
E. Ghavanloo, S.A. Fazelzadeh, Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect. Appl. Math. Model. 36, 4988–5000 (2012)
Y.Y. Zhang, C.M. Wang, W.H. Duan, Y. Xiang, Z. Zong, Assessment of continuum mechanics models in predicting buckling strains of single-walled carbon nanotubes. Nanotechnology 20, 395707 (2009)
Y.Y. Zhang, V.B.C. Tan, C.M. Wang, Effect of chirality on buckling behavior of single-walled carbon nanotubes. J. Appl. Phys. 100, 074304 (2006)
C.M. Wang, Y.Y. Zhang, Y. Xiang, J.N. Reddy, Recent studies on buckling of carbon nanotubes. Appl. Mech. Rev. 63, 030804 (2010)
D.D.T.K. Kulathunga, K.K. Ang, J.N. Reddy, Accurate modeling of buckling of single- and double-walled carbon nanotubes based on shell theories. J. Phys. Condens. Matter 21, 435301 (2009)
C.M. Wang, Z.Y. Tay, A.R. Chowdhuary, W.H. Duan, Y.Y. Zhang, N. Silvestre, Examination of cylindrical shell theories for buckling of carbon nanotubes. Int. J. Struct. Stab. Dyn. 11, 1035–1058 (2011)
R. Ansari, S. Sahmani, H. Rouhi, Rayleigh–Ritz axial buckling analysis of single-walled carbon nanotubes with different boundary conditions. Phys. Lett. A 375, 1255–1263 (2011)
L.F. Wang, Q.S. Zheng, J.Z. Liu, Q. Jiang, Size dependence of the thin-shell model for carbon nanotubes. Phys. Rev. Lett. 95, 105501 (2005)
H.S.P. Wong, D. Akinwande, Carbon Nanotube and Graphene Device Physics (Cambridge University Press, Cambridge, 2011)
V.N. Popov, Carbon nanotubes: properties and application. Mat. Sci. Eng. R 43, 61–102 (2004)
M. Mitra, S. Gopalakrishnan, Vibrational characteristics of single-walled carbon-nanotube: time and frequency domain analysis. J. Appl. Phys. 101, 114320 (2007)
V. Sundararaghavan, A. Waas, Non-local continuum modeling of carbon nanotubes: physical interpretation of non-local kernels using atomistic simulations. J. Mech. Phys. Solids 59, 1191–1203 (2011)
E. Ghavanloo, S.A. Fazelzadeh, H. Rafii-Tabar, Analysis of radial breathing-mode of nanostructures with various morphologies: a critical review. Int. Mater. Rev. 60, 312–329 (2015)
C. Thomsen, S. Reich, Double resonant Raman scattering in graphite. Phys. Rev. Lett. 85, 5214–5217 (2000)
L. Li, T. Chang, Explicit solution for G-band mode frequency of single-walled carbon nanotubes. Acta Mech. Solida Sin. 22, 571–583 (2009)
M.S. Dresselhaus, P.C. Eklund, Phonons in carbon nanotubes. Adv. Phys. 49, 705–814 (2000)
H. Kuzmany, W. Plank, M. Hulman, C. Kramberger, A. Gruneis, T. Pichler, H. Peterlik, H. Kataura, Y. Achiba, Determination of SWCNT diameters from the Raman response of the radial breathing mode. Eur. Phys. J. B 22, 307–320 (2001)
J. Maultzsch, H. Telg, S. Reich, C. Thomsen, Radial breathing mode of single-walled carbon nanotubes: optical transition energies and chiral-index assignment. Phys. Rev. B 72, 205438 (2005)
P.T. Araujo, P.B.C. Pesce, M.S. Dresselhaus, K. Sato, R. Saito, A. Jorio, Resonance Raman spectroscopy of the radial breathing modes in carbon nanotubes. Phys. E 42, 1251–1261 (2010)
D. Zhang, J. Yang, M. Li, Y. Li, (\(n\), \(m\)) assignments of metallic single-walled carbon nanotubes by Raman spectroscopy: the importance of electronic Raman scattering. ACS Nano 10, 10789–10797 (2016)
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Ghavanloo, E., Rafii-Tabar, H., Fazelzadeh, S.A. (2019). Modelling the Mechanical Characteristics of Carbon Nanotubes: A Nonlocal Differential Approach. In: Computational Continuum Mechanics of Nanoscopic Structures. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-11650-7_9
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