About definition of the elasticity module of single-walled carbon nanotubes by methods of structural mechanics





elasticity module, single-walled carbon nanotubes, molecular mechanics, structural mechanics, numerical modeling


The purpose of article is working off and check of numerical techniques of definition of the elasticity module of single-walled carbon nanotubes with use of a method of final elements, and also ties between parameters of molecular and structural mechanics. Researches were conducted for nanotubes of various types of spatial and frame models, namely the armchaіr type, the zigzag type and the chіral type. Program codes with use of freely open software of Gmsh are developed for design of models of nanotubes of these types. Formulations of linear and nonlinear ratios for determination of parameters of structural mechanics on the basis of energy potentials and power coefficients of molecular mechanics are considered. The formulation of a nonlinear problem received a certain specification regarding definition of ratios "the generalized deformation – the generalized tension". The numerical models for research of the elasticity module of nanotubes of various dimension-types (chіrality and diameter) representing macroes in the APDL ANSYS Mechanical APDL programming language are developed. Results of comparison of the received results showed satisfactory coordination with theoretical and experimental data: the divergence with the known theoretical estimates makes 0.08–5.1 %. The offered verified numerical techniques for definition of the elasticity module of nanotubes are planned to be used further for development of new polymeric nanocomposites.

Author Biographies

Anton Karvatskii, Igor Sikorsky Kyiv Polytechnic Institute, Kyiv

ІХФ, кафедра ХПСМ, професор

Ihor Mikulionok, Igor Sikorsky Kyiv Polytechnic Institute, Kyiv

ІХФ, кафедра ХПСМ, професор

Taras Lazarev, State Enterprise "Design Bureau" South "named after M.K. Yangel

провідний науковий співробітник

Kateryna Korolenko, Igor Sikorsky Kyiv Polytechnic Institute, Kyiv

студентка 1 курсу магістратури, каф. ХПСМ, ІХФ


  1. Iijima, S. (1991), “Helical microtubules of graphitic carbon”, Nature, London, no. 354, pp. 56-58. https://doi.org/10.1038/354056a0
  2. Lau, K.-T. and Hui, D. (2002), “The revolutionary creation of new advanced materials - carbon nanotube composites”, Composites Part B: Engineering, vol. 33, pp. 263-277.
  3. Yu, M.-F., Lourie, O., and dr. (2000), “Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load,” Science, vol. 287, no. 5453, pp. 637-640. https://doi.org/10.1126/science.287.5453.637
  4. Tombler, T. W., Zhou, C. and dr. (2000), “Reversible electromechanical characteristics of carbon nanotubes under local- probe manipulation,” Nature, vol. 405, no. 6788, pp. 769-772. https://doi.org/10.1038/35015519
  5. Bian, L. and Zhao, H. (2015), “Elastic properties of a single-walled carbon nanotube under a thermal environment,” Composite Structures, vol. 121, pp. 337-343. https://dx.doi.org/10.1016/j.compstruct.2014.11.032
  6. Wenxing, B., Changchun, Z. and Wanzhao, C. (2004), “Simulation of Young’s modulus of single-walled carbon nanotubes by molecular dynamics,” Physica B: Condensed Matter, vol. 352, No. 1-4, pp. 156-163. https://doi.org/10.1016/j.physb.2004.07.005
  7. Lier, G.V., Alsenoy, C.V., Doren, V.V. and Geerlings, P. (2000), “Ab initio study of the elastic properties of single-walled carbon nanotubes and grapheme”, Chemical Physics Letters, vol. 326(1-2), pp. 181-185. https://doi.org/10.1016/S0009-2614(00)00764-8" target="_blank">https://doi.org/10.1016/S0009-2614(00)00764-8
  8. Li, C. and Chou, T.-W. (2003), “A structural mechanics approach for the analysis of carbon nanotubes“, International Journal of Solids and Structures, vol. 40, pp. 2487-2499. https://doi.org/10.1016/S0020-7683(03)00056-8
  9. Tserpes, K.I. and Papanikos, P. (2005). “Finite element modeling of single-walled carbon nanotubes”, Composites: Part B, vol. 36, pp. 468-477. https://doi.org/10.1016/j.compositesb.2004.10.003
  10. Lu, X. and Hu, Z. (2012), “Mechanical property evaluation of single-walled carbon nanotubes by finite element modeling” Composites: Part B, Engineering, vol. 43, no. 4, pp. 1902-1913. https://doi.org/10.1016/j.compositesb.2012.02.002
  11. Meo, M. and Rossi, M. (2006), “Prediction of Young’s modulus of single wall carbon nanotubes by molecular-mechanics based finite element modeling”, Composites Science and Technology, vol. 66, pp. 1597-1605. https://doi.org/10.1016/j.compscitech.2005.11.015
  12. Rossi, M. and Meo, M. (2009), “On the estimation of mechanical properties of single-walled carbon nanotubes by using a molecular-mechanics based FE approach,” Compos. Sci. Technol., vol. 69, no. 9, pp. 1394-1398. https://doi.org/10.1016/j.compscitech.2008.09.010
  13. Esbati, A.H. and Irani, S. (2017), “Failure analysis of carbon nanotubes with a Stone-Wales defect using nonlinear finiteelement methods”, Mechanics of Composite Materials, vol. 53, no. 5, pp. 631-644. https://doi.org/10.1007/s11029-017-9692-6
  14. Thompson, M. and Thompson, J. (2017), ANSYS Mechanical APDL for Finite Element Analysis, 1st edn., Butterworth-Heinemann, Oxford, UK.
  15. Belytschko, T., Xiao, S.P., Schatz, G.C. and Ruoff, R.S. (2002), “Atomistic simulations of nanotube fracture”, Phys. Rev. B, vol. 65, pp. 235430-1-8. https://doi.org/10.1103/PhysRevB.65.235430
  16. Chang, T. and Gao, H. (2003),”Size dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model”, J. Mech. Phys. Solids, vol. 51, pp. 1059-1074. https://doi.org/10.1016/S0022-5096(03)00006-1
  17. Koloczek, J., Young-Kyun, K. and Burian, A. (2001), “Characterization of spatial correlations in carbon nanotubes-modelling studies” Journal of Alloys and Compounds, vol. 328, no. 1-2, pp. 222-225. https://doi.org/10.1016/S0925-8388(01)01298-1
  18. Gmsh. A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. URL:http://geuz.org/gmsh/ (Last access: 10.12.2018)



How to Cite

A. Karvatskii, I. Mikulionok, T. Lazarev, and K. Korolenko, “About definition of the elasticity module of single-walled carbon nanotubes by methods of structural mechanics”, Mech. Adv. Technol., no. 1(85), pp. 13–25, Apr. 2019.



Original study