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Elastic Buckling Behaviour of General Multi-Layered Graphene Sheets

Aerospace Engineering Division, School of Mechanical and Aerospace Engineering, Nanyang Technological University, 639798 Singapore

Special Issues: Modeling Materials Behavior at the Mesoscale

Elastic buckling behaviour of multi-layered graphene sheets is rigorously investigated. Van der Waals forces are modelled, to a first order approximation, as linear physical springs which connect the nodes between the layers. Critical buckling loads and their associated modes are established and analyzed under different boundary conditions, aspect ratios and compressive loading ratios in the case of graphene sheets compressed in two perpendicular directions. Various practically possible loading configurations are examined and their effect on buckling characteristics is assessed. To model more accurately the buckling behaviour of multi-layered graphene sheets, a physically more representative and realistic mixed boundary support concept is proposed and applied. For the fundamental buckling mode under mixed boundary support, the layers with different boundary supports deform similarly but non-identically, leading to resultant van der Waals bonding forces between the layers which in turn affect critical buckling load. Results are compared with existing known solutions to illustrate the excellent numerical accuracy of the proposed modelling approach. The buckling characteristics of graphene sheets presented in this paper form a comprehensive and wholesome study which can be used as potential structural design guideline when graphene sheets are employed for nano-scale sensing and actuation applications such as nano-electro-mechanical systems.
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References

1. Geim AK, Novoselov KS (2007) The rise of graphene. Nature Mater 6: 183-191.    

2. Novoselov KS, Geim AK, Morozov SV, et al. (2004) Electric field effect in atomically thin carbon films. Science 306: 666-669.    

3. Bunch JS, van der Zande1 AM, Verbridge SS, et al. (2007) Electromechanical resonators from graphene sheets. Science 315: 490-493.    

4. Garcia-Sanchez D, van der Zande AM, Paulo AS, et al. (2008) Imaging mechanical vibration in suspended graphene sheets. Nano Lett 8: 1399-1403.    

5. Chen C, Rosenblatt S, Bolotin KI, et al. (2009) Performance of monolayer graphene mechanical resonators with electrical readout. Nature Nanotech 4: 861-867.    

6. van der Zande AM, Barton RA, Alden JS, et al. (2010) Large-scale arrays of single-layer graphene resonators. Nano Lett 10: 4869-4873.    

7. Singh V, Sengupta S, Solanki1 HS, et al. (2010) Probing thermal expansion of graphene and modal dispersion at low-temperature using graphene nano-electro-mechanical systems resonators. Nanotechnology 21: 165204.    

8. Song XF, Oksanen M, Sillanpää MA, et al. (2012) Stamp transferred suspended graphene mechanical resonator for radio frequency electrical readout. Nano Lett 12: 198-202.    

9. Sakhaee-Pour A, Ahmadian MT, Vafai A (2008) Potential application of single-layered graphene sheet as strain sensor. Solid State Commun 147: 336-340.    

10. Dan YP, Lu Y, Kybert NJ, et al. (2009) Intrinsic response of graphene vapour sensors. Nano Lett9: 1472-1475.

11. Cheng ZG, Li Q, Li ZJ, et al. (2010) Suspended graphene sensors with improved signal and reduced noise. Nano Lett 10: 1864-1868.    

12. Lu Y, Goldsmith BR, Kybert N, et al. (2010) DNA-decorated graphene chemical sensors. Appl Phys Lett 97: 083107.    

13. Ijima S, Brabec C, Maiti A, et al. (1996) Structural flexibility of carbon nanotubes. J Chem Phys104: 2089-2092.

14. Hernandez E, Goze C, Bernier P, et al. (1998) Elastic properties of C and BxCyNz composite nanotubes. Phys Rev Lett 80: 4502-4505.    

15. Sanchez-Portal D, Artacho E, Soler JM, et al. (1999) Ab initio structural, elastic, and vibrational properties of carbon nanotubes. Phys Rev B 59: 12678-12688.    

16. Govindjee S, Sackman JL (1999) On the use of continuum mechanics to estimate the properties of nanotubes Solid State Commun 110: 227-230.

17. Yoon J, Ru CQ, Mioduchowski A (2003) Vibration of an embedded multiwall carbon nanotube. Composite Sci Technol 63: 1533-1545.    

18. Ru CQ (2000) Effective bending stiffness of carbon nanotubes. Phys Rev B 62: 9973-9976.    

19. Li C, Chou TW (2003) A structural mechanics approach for the analysis of carbon nanotubes. Int J Solids Structures 40: 2487-2499.    

20. Chowdhury R, Adhikari S, Scarpa F, et al. (2011) Transverse vibration of single-layer graphene sheets. J Phys D—Appl Phys 44: 205401

21. Pradhan SC, Sahu B (2010) Vibration of single layer graphene sheet based on non-local elasticity and higher order shear deformation theory. J Comp Theor Nanosci 7: 1042-1050.    

22. Murmu T, Pradhan SC (2009) Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory. J Appl Phys 105: 064319.    

23. Sakhaee-Pour A (2009) Elastic buckling of single-layered graphene sheet. Comp Mater Sci 45:266-270.    

24. Pradhan SC, Murmu T (2009) Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum theory. Comp Mater Sci 47: 268-274.    

25. Pradhan SC (2009) Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory. Phys Lett A 373: 4182-4188.    

26. Pradhan SC, Murmu T (2010) Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory. Physica E-Low Dimensional System Nanostructures 42: 1293-1301.    

27. Kumar S, Hembram KPSS, Waghmare UV (2010) Intrinsic buckling strength of graphene: Firstprinciples density functional theory calculations. Phys Rev B 82: 11-15.

28. Wilber JP (2010) Buckling of Graphene Layers Supported by Rigid Substrates. J Comp Theor Nanosci 7: 2338-2348.    

29. Taziev RM, Prinz VY (2011) Buckling of a single-layered graphene sheet on an initially strained InGaAs thin plate. Nanotechnology 22: 305705.    

30. Farajpour A, Mohammadi M, Shahidi AR, et al. (2011) Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model. Pysical E-Low-Dimensional Systems Nanotechnologies 43: 1820-1825.    

31. Samaei AT, Abbasion S, Mirsayar MM (2011) Buckling analysis of a single-layer graphene sheet embedded in an elastic medium based on nonlocal Mindlin plate theory. Mech Res Commun 38:481-485.    

32. Ansari R, Rouhi H (2012) Explicit analytical expressions for the critical buckling stresses in a monolayer graphene sheet based on nonlocal elasticity. Solid State Commun 152: 56-59.    

33. Rouhi S, Ansari R (2012) Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets. Physica E-Low-Dimensional Systems Nanostructures44: 764-772.

34. Girifalco LA, Lad RA (1956) Energy of Cohesion, Compressibility, and the Potential Energy Functions of the Graphite System. J Chem Phys 25: 693-697.    

35. Jomehzadeh E, Saidi AR (2011) A study on large amplitude vibration of multilayered graphene sheets. Comp Mater Sci 50: 1043-1051.    

36. Saito R, Matsuo R, T Kimura, et al. (2001) Anomalous potential barrier of double-wall carbon nanotube. Chem Phys Lett 348: 187-193.    

37. Shu C, Richards BE (1992) Application of Generalized Differential Quadrature to Solve Two- Dimensional Imcompressible Navier-Stokes Equations. Int J Numerical Methods Fluids 15: 791-798.    

38. Du H, Lim MK, Lin RM (1995) Application of Generalized Differential Quadrature to Vibration Analysis. J Sound and Vibration 181: 279-293.    

39. Shu C (2000) Differential Quadrature and Its Application in Engineering, London, Springer- Verlag.

40. Timoshenko SP, Gere JM (1961) Theory of Elastic Stability, New York, McGraw-Hill.

41. Lin RM, Lim MK, Du H (1994) Large Deflection Analysis of Plates Under Thermal Loading. Comp Method Appl Mech Eng 117: 381-390.    

42. Rouhi S, Ansari R (2012) Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets. Physica E-Low-Dimensional Systems Nanostructures44: 764-772.

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