Numerical Investigation of Size and Structure Effect on Tensile Characteristics of Symmetric and Asymmetric CNTs

Document Type : Research Paper


Aerospace Engineering Department, K.N.Toosi University of Technology, Tehran, 16765-3381, Iran


In this research, the influence of structure on the tensile properties of single- walled carbon nanotubes (CNTs) is evaluated using molecular mechanics technique and finite element method. The effects of diameter, length and chiral angle on elastic modulus and Poisson’s ratio of armchair, zigzag and chiral structures are investigated. To simulate the CNTs, a 3D FEM code is developed using the ANSYS commercial software. Considering the carbon-carbon covalent bonds as connecting load-carrying beam elements, and the atoms as joints of the elements, CNTs are simulated as space-frame structures. The atomic potentials are estimated using harmonic simple functions. The numerical results show that by increasing the diameter and length to a certain amount, the size effect on tensile behavior of modeled nanotubes is omitted. In fact, for nanotubes with diameter over 2 nm and length over 36.5 nm the chiral angle is the only effective factor on the tensile properties. Also, it is found that the structure has a little effect on the elasticity modulus, which is about 4%. However, Poisson’s ratio can be affected significantly with chiral angle. Asymmetric structures with angles θ <18˚ show higher Poisson’s ratio in comparison with the other structures, such that it can be 16% larger for little chirality CNTs than armchair.


1. Iijima S. Helical microtubules of graphitic carbon. nature.1991;354(6348):56-8.
2. Yakobson BI, Brabec CJ, Bernholc J. Nanomechanics of carbon tubes: instabilities beyond linear response. Physical review letters. 1996;76(14):2511.
3. Odegard GM, Gates TS, Nicholson LM, Wise KE. Equivalentcontinuum modeling of nano-structured materials.
Composites Science and Technology. 2002;62(14):1869-80.
4. Li C, Chou TW. A structural mechanics approach for the analysis of carbon nanotubes. International Journal of Solids and Structures. 2003;40(10):2487-99.
5. Xiao JR, Gama BA, Gillespie JW. An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes. International Journal of Solids and Structures. 2005;42(11):3075-92.
6. Ávila AF, Lacerda GS. Molecular mechanics applied to single-walled carbon nanotubes. Materials Research. 2008;11(3):325-33.
7. Tserpes KI, Papanikos P. Finite element modeling of singlewalled carbon nanotubes. Composites Part B: Engineering. 2005;36(5):468-77.
8. Zaeri MM, Ziaei-Rad S, Vahedi A, Karimzadeh F. Mechanical modelling of carbon nanomaterials from nanotubes to buckypaper. Carbon. 2010;48(13):3916-30.
9. Shokrieh MM, Rafiee R. Prediction of Young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach. Materials & Design. 2010;31(2):790-5.
10. Lu X, Hu Z. Mechanical property evaluation of single-walled carbon nanotubes by finite element modeling. Composites Part B: Engineering. 2012;43(4):1902-13.
11. Gogotsi Y, editor. Nanomaterials handbook. CRC press; 2006.
12. Kalamkarov AL, Georgiades AV, Rokkam SK, Veedu VP, Ghasemi-Nejhad MN. Analytical and numerical techniques to predict carbon nanotubes properties. International journal of Solids and Structures. 2006;43(22):6832-54.
13. Rafii-Tabar H. Computational modelling of thermomechanical and transport properties of carbon nanotubes. Physics Reports. 2004;390(4):235-452.
14. Gelin BR. Molecular modeling of polymer structures and properties. Hanser Publishers; Hanser/Gardner Publications; 1994.
15. Cornell WD, Cieplak P, Bayly CI, Gould IR, Merz KM, Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA. A second generation force field for the simulation of proteins, nucleic acids, and organic molecules. Journal of the American Chemical Society. 1995;117(19):5179-97.
16. Gaddamanugu D. M.Sc. Thesis. Texas A & M University.2009.
17. Giannopoulos GI, Kakavas PA, Anifantis NK. Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach. Computational Materials Science. 2008;41(4):561-9.
18. Yang QS, Li BQ, He XQ, Mai YW. Modeling the mechanical properties of functionalized carbon nanotubes and their composites: design at the atomic level. Advances in Condensed Matter Physics. 2014;482056;doi: 10.1155/2014/482056.
19. Lu JP. Elastic properties of carbon nanotubes and nanoropes. Physical Review Letters. 1997;79(7):1297.
20. Sun X, Zhao W. Prediction of stiffness and strength of singlewalled carbon nanotubes by molecular-mechanics based finite element approach. Materials Science and Engineering:A. 2005;390(1):366-71.
21. Natsuki T, Tantrakarn K, Endo M. Effects of carbon nanotube structures on mechanical properties. Applied Physics A. 2004;79(1):117-24.