Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Glukhova O. E., Glukhova O. E., Kossovich E. L., Fadeev A. A. Mechanical properties study for graphene sheets of various size. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2012, vol. 12, iss. 4, pp. 63-66. DOI: 10.18500/1816-9791-2012-12-4-63-66

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
Full text:
(downloads: 165)

Mechanical properties study for graphene sheets of various size

Glukhova Ol'ga Evgen'evna, Saratov State University
Glukhova Ol'ga Evgen'evna, Saratov State University
Kossovich Elena Leonidovna, Saratov State University
Fadeev Aleksandr Andreevich, Saratov State University

We studied mechanical properties of large graphene sheets. The Young's modulus was found for each of the considered nanoparticles and sheets. To this end, the deformation was applied in two orthogonal directions – zigzag and armchair directions of the graphene atomic framework. It was established that there exist a size effect on the Young's modulus of graphene. Also, it was found that themechanical properties of graphene become close to isotropic ones when the linear dimensions of the latter are large enough for it to be considered as a macro-particle. Also, under these conditions, the Young's modulus becomes close to 1.1 TPa. 

  1. Griffith A. A. The phenomena of rupture and flow in solids // Philosophical Transactions of the Royal Society of London. Ser. A. 1921. Vol. 221. P. 163–198.
  2. Cowie J. M. G Polymers : Chemistry and Physics of Modern Materials. N.Y. : Blackie Academic, 1991. 436 p.
  3. Geim A. K. Graphene : status and prospects // Science. 2009. Vol. 324. P. 5934.
  4. Jiang J. -W., Wang J. -S., Li B. Young’s modulus of graphene : a molecular dynamics study // Phys. Rev. Ser. B. 2009. Vol. 80. P. 113–405.
  5. Lee C., Wei X., Kysar J. W, Hone J. Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene // Science. 2008. Vol. 321. P. 385.
  6. Reddy C. D., Rajendran S., Liew K. M. Equilibrium configuration and continuum elastic properties of finite sized graphene // Nanotechnology. 2006. Vol. 17. P. 864–870.
  7. Arroyo M., Belytschko T. Finite crystal elasticity of carbon nanotubes based o n the exponential Cauchy–Born rule // Phys. Rev. B. 2004. Vol. 69. P. 115415.
  8. Brenner D. W. Empirical Potential for Hydrocarbons for Use in Simulating the Chemical Vapor Deposition of Diamond Films // Phys. Rev. Ser. B. 1990. Vol. 42. P. 9458–9471.
  9. Brenner D. W., Shenderova O. A., Harrison J. A., Stuart S. J., Ni B., Sinnott S. B. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons // J. Phys. : Condens. Matter. 2002. Vol. 14. P. 783–802.
  10. Kudin K. N., Scuseria G. E. and Yakobson B. I. C2F, BN and C nanoshell elasticity from ab initio computations // Phys. Rev. Ser. B. 2001. Vol. 64. P. 235406.
  11. Shimpi R. P., Patel H. G. A two variable refined plate theory for orthotropic plate analysis // Intern. J. Solids and Structures. 2006. Vol. 43, iss. 22–23. P. 6783–6799.
  12. Tsiatas G. C., Yiotis A. J. A microstructure-dependent orthotropic plate model based on a modified couple stress theory // Recent Developments in Boundary Element Methods : A Volume to Honour Professor John T. Katsikadelis / ed. E. J. Sapountzakis. Southampton : WIT Press, 2010. P. 295–308.
  13. Setoodeh A. R., Malekzadeh P., Vosoughi A. R. Nonlinear free vibration of orthotropic graphene sheets using nonlocal Mindlin plate theory // Proc. Mech. Part C : J. Mechanical Engineering Science. 2012.Vol. 226. P. 1896–1906.
  14. Narendar S., Gopalakrishnan S. Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory // Acta Mech. 2012. Vol. 223. P. 395–413.
  15. Wang Q. Effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes //Intern. J. Solid Struct. 2004. Vol. 41. P. 5451–5461.
  16. Shokrieh M. M., Rafiee R. Prediction of Young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach // Materials and Design. 2010. Vol. 31. P. 790–795.
  17. Глухова О. Е., Терентьев О. А. Теоретическое исследование электронных и механических свойств C-N однослойных нанотрубок // Физика волновых процессов и радиотехнические системы. 2007. Т. 10, № 4.С. 85–89.
  18. Глухова О. Е. Жесткость Y-образных углеродных нанотрубок при деформации растяжения/сжатия // Нано- и микросиcтемная техника. 2009. № 1. С. 19–22.
  19. Das S., Seelaboyina R., Verma V., Lahiri I., Hwang J. Y., Benerjee R., Choi W. Synthesis and characterization of self-organized multilayered graphenecarbon nanotube hybrid films // J. Mater. Chem. 2011. Vol. 21. P 7289–7295.