Coupled systems mechanics

  • 제4권2호
  • /
  • Pages.137-155
  • /
  • 2015
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Homogenized elastic properties of graphene for moderate deformations

  • Marenic, Eduard (Sorbonne Universites/Universite de Technologie de Compiegne Chaire de Mecanique, Lab. Roberval de Mecanique) ;
  • Ibrahimbegovic, Adnan (Sorbonne Universites/Universite de Technologie de Compiegne Chaire de Mecanique, Lab. Roberval de Mecanique)
  • 투고 : 2015.05.05
  • 심사 : 2015.06.07
  • 발행 : 2015.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a simple procedure to obtain a substitute, homogenized mechanical response of single layer graphene sheet. The procedure is based on the judicious combination of molecular mechanics simulation results and homogenization method. Moreover, a series of virtual experiments are performed on the representative graphene lattice. Following these results, the constitutive model development is based on the well-established continuum mechanics framework, that is, the non-linear membrane theory which includes the hyperelastic model in terms of principal stretches. A proof-of-concept and performance is shown on a simple model problem where the hyperelastic strain energy density function is chosen in polynomial form.

키워드

참고문헌

  1. Abraham, R. and Marsden, J. E. (1987), Foundations of mechanics, Addison-Wesley.
  2. Arroyo, M. and Belytschko, T. (2002), "An atomistic-based finite deformation membrane for single layer crystalline films", J. Mech. Phys. Solids, 50(9), 1941-1977. https://doi.org/10.1016/S0022-5096(02)00002-9
  3. Atkins, P. and De Paula, J. (2006), Physical Chemistry, Oxford University Press, 8rev ed edition.
  4. Belytschko, T., Liu, W. K. and Moran, B. (2000), Nonlinear Finite Elements for Continua and Structures. Wiley.
  5. Belytschko, T., Xiao, S.P., Schatz, G.C. and Ruoff, R.S. (2002), "Atomistic simulations of nanotube fracture", Phys. Rev. B, 65(23), 235430. https://doi.org/10.1103/PhysRevB.65.235430
  6. Brenner, D.W. (1990), "Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films", Phys. Rev. B, 42, 9458-9471. https://doi.org/10.1103/PhysRevB.42.9458
  7. Brenner, D.W., Shenderova, O.A., Harrison, J.A., Stuart, S.J., Ni, B. and Sinnott, S.B. (2002), "A second-generation reactive empirical bond order (rebo) potential energy expression for hydrocarbons", J. Phys.: Condensed Matter, 14(4), 783. https://doi.org/10.1088/0953-8984/14/4/312
  8. Bedoui, F. and Cauvin, L. (2012), "Elastic properties prediction of nano-clay re- inforced polymers using hybrid micromechanical models", Comput. Mater. Sci., 65, 309-314. https://doi.org/10.1016/j.commatsci.2012.07.023
  9. Cadelano, E., Palla, P.L., Giordano, S. and Colombo, L. (2009), "Nonlinear elasticity of monolayer grapheme", Phys. Rev. Lett., 102, 235502. https://doi.org/10.1103/PhysRevLett.102.235502
  10. Caillerie, D., Mourat, A. and Raoult, A. (2006), "Discrete homogenization in graphene sheet modeling", J. Elasticity, 84, 33-68. https://doi.org/10.1007/s10659-006-9053-5
  11. Ericksen, J. (2008), "On the cauchyborn rule", Math. Mech.Solids, 13, 199-220. https://doi.org/10.1177/1081286507086898
  12. Ericksen, J.L. (1984), "The cauchy and born hypotheses for crystals. Phase transformation and material instabilities in solids" - from book 'Mechanics and Mathematics of Crystals: Selected Papers of J. L. Ericksen' by Millard F. Beatty and Michael A. Hayes, page 6177.
  13. Geim, A.K. and Novoselov, K.S. (2007), "The rise of grapheme", Nature Mater., 6, 183-191. https://doi.org/10.1038/nmat1849
  14. Gelineau, P., Stepie, M., Weigand, S., Cauvin, L. and Bdoui, F. (2015), "Elastic properties prediction of nano-clay reinforced polymer using multi-scale modeling based on a multi-scale characterization", Mech. Mater., 89, 12- 22. https://doi.org/10.1016/j.mechmat.2015.03.013
  15. Georgantzinos, S., Giannopoulos, G. and Anifantis, N. (2010), "Numerical investigation of elastic mechanical properties of graphene structures", Mater. Des., 31(10), 4646 -4654. https://doi.org/10.1016/j.matdes.2010.05.036
  16. Gmez, H., Ram, M.K., Alvi, F., Villalba, P., Stefanakos, E.L. and Kumar, A. (2011), "Graphene-conducting polymer nanocomposite as novel electrode for supercapacitors", J. Power Sources, 196(8), 4102 -4108. https://doi.org/10.1016/j.jpowsour.2010.11.002
  17. Hu, K., Kulkarni, D.D., Choi, I. and Tsukruk, V.V. (2014), "Graphene-polymer nanocom- posites for structural and functional applications", Progress in Polymer Sci., 39(11), 1934- 1972. https://doi.org/10.1016/j.progpolymsci.2014.03.001
  18. Huang, Y., Wu, J. and Hwang, K.C. (2006), "Thickness of graphene and single-wall carbon nanotubes", Phys. Rev. B, 74, 245413. https://doi.org/10.1103/PhysRevB.74.245413
  19. Huet, C. (1990), "Application of variational concepts to size effects in elastic heterogeneous bodies", J. Mech. Phys. Solids, 38(6), 813- 841. https://doi.org/10.1016/0022-5096(90)90041-2
  20. Ibrahimbegovic, A. (1994), "Finite elastoplastic deformations of space-curved membranes", Comput. Method. Appl. M., 119, 371-394. https://doi.org/10.1016/0045-7825(94)90096-5
  21. Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics, Springer.
  22. Ibrahimbegovic, A. and Gruttmann, F. (1993), "A consistent finite element formulation of nonlinear membrane shell theory with particular reference to elastic rubberlike material", Finite Elem. Anal. Des., 12, 75-86.
  23. Lee, C., Wei, X., Kysar, J. and Hone, J. (2008), "Measurement of the elastic properties and intrinsic strength of monolayer graphene", Science, 321(5887), 385-388. https://doi.org/10.1126/science.1157996
  24. Lu, Q., Gao, W. and Huang, R. (2011), "Atomistic simulation and continuum modeling of graphene nanoribbons under uniaxial tension", Model. Simul. Mater. Sc., 19(5), 054006. https://doi.org/10.1088/0965-0393/19/5/054006
  25. Lu, Q. and Huang, R. (2009), "Nonlinear mechanics of single-atomic-layer grephene sheets", Int. J. Appl. Mech., 1, 443-467. https://doi.org/10.1142/S1758825109000228
  26. Marenic, E., Ibrahimbegovic, A., Soric, J. and Guidault, P.A. (2013), "Homogenized elastic properties of graphene for small deformations", Materials: Special Issue "Computational Modeling and Simulation in Materials Study", 6(9), 3764-3782.
  27. Markovic, D. and Ibrahimbegovic, A. (2004), "On micro-macro inter- face conditions for micro scale based FEM for inelastic behavior of heterogeneous materials", Comput. Method. Appl. M., 193(48-51), 5503-5523. https://doi.org/10.1016/j.cma.2003.12.072
  28. Morse, P.M. (1929), "Diatomic molecules according to the wave mechanics. ii. vibrational levels", Phys. Rev., 34, 57-64. https://doi.org/10.1103/PhysRev.34.57
  29. Novoselov, K.S., Jiang, D., Schedin, F., Booth, T.J., Khotkevich, V.V., Morozov, S.V. and Geim, A.K. (2005), "Two-dimensional atomic crystals", PNAS, 102-30, 10451-10453.
  30. Reddy, C.D., Rajendran, S. and Liew, K.M. (2006), "Equilibrium configuration and continuum elastic properties of finite sized grapheme", Nanotechnology, 17(3), 864. https://doi.org/10.1088/0957-4484/17/3/042
  31. Ruoff, R.S., Qian, D. and Liu, W.K. (2003), "Mechanical properties of carbon nanotubes: theoretical predictions and experimental measurements", Comptes Rendus Physique, 4(9), 993-1008. https://doi.org/10.1016/j.crhy.2003.08.001
  32. Singh, V., Joung, D., Zhai, L., Das, S., Khondaker, S.I. and Seal, S. (2011), "Graphene based materials: Past, present and future", Prog. Mater. Sci., 56(8), 1178 -1271. https://doi.org/10.1016/j.pmatsci.2011.03.003
  33. Stankovich, S., Dikin, D.A., Dommett, G.H.B., Kohlhaas, K.M., Zimney, E.J., Stach, E.A., Piner, R.D., Nguyen, S.T. and Ruoff, R.S. (2006), "Graphene-based composite materials", Nature, 442(7100), 282-286. https://doi.org/10.1038/nature04969
  34. Tersoff, J. (1986), "New empirical model for the structural properties of silicon", Phys. Rev. Lett., 56, 632-635. https://doi.org/10.1103/PhysRevLett.56.632
  35. Topsakal, M. and Ciraci, S. (2010), "Elastic and plastic deformation of graphene, silicene, and boron nitride honeycomb nanoribbons under uniaxial tension: A first-principles density- functional theory study", Phys. Rev. B, 81, 024107. https://doi.org/10.1103/PhysRevB.81.024107
  36. Volokh, K. (2012), "On the strength of grapheme", J. Appl. Mech.- T ASME, 79, 064501- 5. https://doi.org/10.1115/1.4005582
  37. Wackerfuss, J. (2009), "Molecular mechanics in the context of the finite element method", Int. J. Numer. Mett. Eng., 77, 969-997. https://doi.org/10.1002/nme.2442
  38. Wriggers, P. (2008), Nonlinear Finite Element Methods, Springer.
  39. Xu, Z. (2009), "Graphene nano-ribbons under tension", Journal of Computational and Theoretical Nanoscience, 6, 625-628. https://doi.org/10.1166/jctn.2009.1082
  40. Zanzotto, G. (1996), "The cauchy-born hypothesis, nonlinear elasticity and mechanical twining in crystals", Acta Crystallographica, 52, 839-849. https://doi.org/10.1107/S0108767396006654
  41. Zhang, K. and Arroyo, M. (2013), "Adhesion and friction control localized folding in supported grapheme", J. Appl. Phys., 113, 193501-8. https://doi.org/10.1063/1.4804265
  42. Zhao, H., Min, K. and Aluru, N.. (2009), "Size and chirality dependent elastic properties of graphene nanoribbons under uniaxial tension", Nanoletters, 9-8, 3012-3015.

피인용 문헌

  1. The effect of material density on load rate sensitivity in nonlinear viscoelastic material models pp.1432-0681, 2018, https://doi.org/10.1007/s00419-018-1448-9
  2. On the mechanical characteristics of graphene nanosheets: a fully nonlinear modified Morse model vol.31, pp.11, 2020, https://doi.org/10.1088/1361-6528/ab598e