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Buckling analysis of multi-layered graphene sheets based on a continuum mechanics model

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Abstract

In this paper, buckling analysis of biaxially compressed multi-layered graphene sheets with a continuum plate model is reported. The equations of motion are analytically solved to obtain closed-form solution for buckling loads of all edges simply supported multi-layered graphene sheets. The interaction of van der Waals (vdWs) pressure between the layers is incorporated in the formulation to determine the buckling behavior of simply supported MLGSs. Explicit formulae are derived for predicting the critical buckling loads of double- and triple-layered graphene sheets, and they clearly indicate the effect of vdW interaction on the critical buckling loads. The critical buckling loads are calculated for various numbers of layered graphene sheets, and the obtained results show that the vdW force has no effect on the first critical buckling load of an MLGS, but plays a significant role in all higher first critical buckling loads for all combinations of m and n.

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References

  1. K.S. Novoselov, A.K. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grigorieva, A. Firsov, Science, 306, 666–669 (2004)

  2. C. Martin-Olmos, H.I. Rasool, B.H. Weiller, J.K. Gimzewski, ACS nano. 7, 4164–4170 (2013)

    Article  Google Scholar 

  3. X. Zang, Q. Zhou, J. Chang, Y. Liu, L. Lin, Microelectron. Eng. 132, 192–206 (2015)

    Article  Google Scholar 

  4. S.K. Georgantzinos, G.I. Giannopoulos, N.K. Anifantis, Mater. Design. 31, 4646–4654 (2010)

  5. L.N. Chen, Solid State Commun. 191, 59–65 (2014)

    Article  ADS  Google Scholar 

  6. M. Sun, Y. Peng, Appl. Surf. Sci. 307, 158–164 (2014)

    Article  Google Scholar 

  7. A.A. Balandin, Nat Mater 10, 569–581 (2011)

    Article  ADS  Google Scholar 

  8. J. Yoon, C. Ru, A. Mioduchowski, Phys. Rev. B 66, 233402 (2002)

    Article  ADS  Google Scholar 

  9. J. Yoon, C. Ru, A. Mioduchowski, Compos. Sci. Technol. 63, 1533–1542 (2003)

    Article  Google Scholar 

  10. C. Wang, C. Ru, A. Mioduchowski, Int J Solids Struct 40, 3893–3911 (2003)

    Article  Google Scholar 

  11. X. He, S. Kitipornchai, K. Liew, J. Mech. Phys. Solids 53, 303–326 (2005)

    Article  ADS  Google Scholar 

  12. X.Q. He, S. Kitipornchai, C. Wang, K. Liew, Int J Solids Struct 42, 6032–6047 (2005)

    Article  Google Scholar 

  13. B.I. Yakobson, C. Brabec, J. Bernholc, Physical review letters 76, 2511 (1996)

    Article  ADS  Google Scholar 

  14. C. Ru, Phys. Rev. B 62, 9973 (2000)

    Article  ADS  Google Scholar 

  15. C. Ru, J. Appl. Phys. 87, 7227–7231 (2000)

    Article  ADS  Google Scholar 

  16. C. Ru, J. Appl. Phys. 89, 3426–3433 (2001)

    Article  ADS  Google Scholar 

  17. C.Q. Ru, J. Mech. Phys. Solids 49, 1265–1279 (2001)

    Article  ADS  Google Scholar 

  18. S. Kitipornchai, X. He, K. Liew, Phys. Rev. B 72, 075443 (2005)

    Article  ADS  Google Scholar 

  19. K. Behfar, R. Naghdabadi, Compos. Sci. Technol. 65, 1159–1164 (2005)

    Article  Google Scholar 

  20. K. Behfar, P. Seifi, R. Naghdabadi, J. Ghanbari, Thin Solid Films 496, 475–480 (2006)

    Article  ADS  Google Scholar 

  21. R. Ansari, B. Arash, H. Rouhi, Compos. Struct. 93, 2419–2429 (2011)

    Article  Google Scholar 

  22. R. Ansari, R. Rajabiehfard, B. Arash, Comput. Mater. Sci. 49, 831–838 (2010)

    Article  Google Scholar 

  23. S. Pradhan, J. Phadikar, Phys. Lett. A 373, 1062–1069 (2009)

    Article  ADS  Google Scholar 

  24. E. Jomehzadeh, A.R. Saidi, Comput. Mater. Sci. 50, 1043–1051 (2011)

    Article  Google Scholar 

  25. A. Sakhaee-Pour, Solid State Commun. 149, 91–95 (2009)

    Article  ADS  Google Scholar 

  26. X.Q. He, J.B. Wang, B. Liu, K.M. Liew, Comput. Mater. Sci. 61, 194–199 (2012)

    Article  Google Scholar 

  27. Z.-B. Shen, H.-L. Tang, D.-K. Li, G.-J. Tang, Comput. Mater. Sci. 61, 200–205 (2012)

    Article  Google Scholar 

  28. M.I. Katsnelson, A.K. Geim, Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 366, 195–204 (2008)

  29. B. Butz, C. Dolle, F. Niekiel, K. Weber, D. Waldmann, H.B. Weber, B. Meyer, E. Spiecker, Nature 505, 533–537 (2014)

    Article  ADS  Google Scholar 

  30. S.K. Jain, G.T. Barkema, N. Mousseau, C.-M. Fang, M.A. van Huis, J. Phys. Chem. C 119, 9646–9655 (2015)

    Article  Google Scholar 

  31. K.J. Sandeep, J. Vladimir, T.B. Gerard, 2D Mater. 4, 015018 (2017)

  32. M. Neek-Amal, P. Xu, J.K. Schoelz, M.L. Ackerman, S.D. Barber, P.M. Thibado, A. Sadeghi, F.M. Peeters, Nat. Commun. 5, 4962 (2014)

    Article  ADS  Google Scholar 

  33. M. Ruiz-García, L.L. Bonilla, A. Prados, J. Stat. Mech: Theory Exp. 2015, 05015 (2015)

    Article  Google Scholar 

  34. M. Ruiz-Garcia, L.L. Bonilla, A. Prados, Phys. Rev. B 94, 205404 (2016)

    Article  ADS  Google Scholar 

  35. L.L. Bonilla, M. Ruiz-Garcia, Phys. Rev. B 93, 115407 (2016)

    Article  ADS  Google Scholar 

  36. J.K. Schoelz, P. Xu, V. Meunier, P. Kumar, M. Neek-Amal, P.M. Thibado, F.M. Peeters, Phys. Rev. B 91, 045413 (2015)

    Article  ADS  Google Scholar 

  37. J.E. Jones, in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, On the determination of molecular fields. I. From the variation of the viscosity of a gas with temperature, vol. 106, no. 738 (The Royal Society, 1924), pp. 441–462

  38. R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical properties of carbon nanotubes (World Scientific, 1998)

  39. R. Saito, R. Matsuo, T. Kimura, G. Dresselhaus, M.S. Dresselhaus. Chem. Phys. Lett. 348, 187–193 (2001)

    Article  ADS  Google Scholar 

  40. X.Q. He, S. Kitipornchai, K.M. Liew, Nanotechnology 16, 2086 (2005)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran

    A. A. Jandaghian & O. Rahmani

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  1. A. A. Jandaghian
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  2. O. Rahmani
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Correspondence to O. Rahmani.

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Jandaghian, A.A., Rahmani, O. Buckling analysis of multi-layered graphene sheets based on a continuum mechanics model. Appl. Phys. A 123, 324 (2017). https://doi.org/10.1007/s00339-017-0881-x

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