The mechanical properties of 2D materials such as monolayer graphene are of extreme importance for several potential applications. We summarize the experimental and theoretical results to date on mechanical loading of freely suspended or fully supported graphene. We assess the obtained axial properties of the material in tension and compression and comment on the methods used for deriving the various reported values. We also report on past and current efforts to define the elastic constants of graphene in a 3D representation. Current areas of research that are concerned with the effect of production method and/or the presence of defects upon the mechanical integrity of graphene are also covered. Finally, we examine extensively the work related to the effect of graphene deformation upon its electronic properties and the possibility of employing strained graphene in future electronic applications.


Article metrics loading...

Loading full text...

Full text loading...


Literature Cited

  1. Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y. 1.  et al. 2004. Electric field effect in atomically thin carbon films. Science 306:666–69 [Google Scholar]
  2. Lee C, Wei XD, Kysar JW, Hone J. 2.  2008. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321:385–88 [Google Scholar]
  3. Novoselov KS, Falko VI, Colombo L, Gellert PR, Schwab MG, Kim K. 3.  2012. A roadmap for graphene. Nature 490:192–200 [Google Scholar]
  4. Androulidakis C, Koukaras EN, Frank O, Tsoukleri G, Sfyris D. 4.  et al. 2014. Failure processes in embedded monolayer graphene under axial compression. Sci. Rep. 4:5271 [Google Scholar]
  5. Frank O, Tsoukleri G, Parthenios J, Papagelis K, Riaz I. 5.  et al. 2010. Compression behavior of single-layer graphenes. ACS Nano 4:3131–38 [Google Scholar]
  6. Mohiuddin TMG, Lombardo A, Nair RR, Bonetti A, Savini G. 6.  et al. 2009. Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grueneisen parameters, and sample orientation. Phys. Rev. B 79:205433–38 [Google Scholar]
  7. Tsoukleri G, Parthenios J, Papagelis K, Jalil R, Ferrari AC. 7.  et al. 2009. Subjecting a graphene monolayer to tension and compression. Small 5:2397–402 [Google Scholar]
  8. Androulidakis C, Tsoukleri G, Koutroumanis N, Gkikas G, Pappas P. 8.  et al. 2014. Experimentally derived axial stress-strain relations for two-dimensional materials such as monolayer graphene. Carbon 81:322–28 [Google Scholar]
  9. Bao W, Myhro K, Zhao Z, Chen Z, Jang W. 9.  et al. 2012. In situ observation of electrostatic and thermal manipulation of suspended graphene membranes. Nano Lett. 12:5470–74 [Google Scholar]
  10. Pereira VM, Neto AHC. 10.  2009. Strain engineering of graphene's electronic structure. Phys. Rev. Lett. 103:046801–4 [Google Scholar]
  11. Huang PY, Ruiz-Vargas CS, van der Zande AM, Whitney WS, Levendorf MP. 11.  et al. 2011. Grains and grain boundaries in single-layer graphene atomic patchwork quilts. Nature 469:389–92 [Google Scholar]
  12. Grantab R, Shenoy VB, Ruoff RS. 12.  2010. Anomalous strength characteristics of tilt grain boundaries in graphene. Science 330:946–48 [Google Scholar]
  13. Wei Y, Wu J, Yin H, Shi X, Yang R, Dresselhaus M. 13.  2012. The nature of strength enhancement and weakening by pentagon–heptagon defects in graphene. Nat. Mater. 11:759–63 [Google Scholar]
  14. Kalosakas G, Lathiotakis NN, Galiotis C, Papagelis K. 14.  2013. In-plane force fields and elastic properties of graphene. J. Appl. Phys. 113:134307 [Google Scholar]
  15. Liu F, Ming PM, Li J. 15.  2007. Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys. Rev. B 76:064120 [Google Scholar]
  16. Cadelano E, Palla PL, Giordano S, Colombo L. 16.  2009. Nonlinear elasticity of monolayer graphene. Phys. Rev. Lett. 102:235502 [Google Scholar]
  17. Wei X, Fragneaud B, Marianetti CA, Kysar JW. 17.  2009. Nonlinear elastic behavior of graphene: ab initio calculations to continuum description. Phys. Rev. B 80:205407 [Google Scholar]
  18. Huang M, Pascal TA, Kim H, Goddard WA, Greer JR. 18.  2011. Electronic−mechanical coupling in graphene from in situ nanoindentation experiments and multiscale atomistic simulations. Nano Lett. 11:1241–46 [Google Scholar]
  19. Koenig SP, Boddeti NG, Dunn ML, Bunch JS. 19.  2011. Ultrastrong adhesion of graphene membranes. Nat. Nanotechnol. 6:543–46 [Google Scholar]
  20. Ferrari AC, Basko DM. 20.  2013. Raman spectroscopy as a versatile tool for studying the properties of graphene. Nat. Nanotechnol. 8:235–46 [Google Scholar]
  21. Frank O, Vejpravova J, Holy V, Kavan L, Kalbac M. 21.  2014. Interaction between graphene and copper substrate: the role of lattice orientation. Carbon 68:440–51 [Google Scholar]
  22. Lee JE, Ahn G, Shim J, Lee YS, Ryu S. 22.  2012. Optical separation of mechanical strain from charge doping in graphene. Nat. Commun. 3:1024 [Google Scholar]
  23. Vlattas C, Galiotis C. 23.  1994. Deformation behaviour of liquid crystal polymer fibres: 1. Converting spectroscopic data into mechanical stress-strain curves in tension and compression. Polymer 35:2335–47 [Google Scholar]
  24. Galiotis C, Paipetis A, Marston C. 24.  1999. Unification of fibre/matrix interfacial measurements with Raman microscopy. J. Raman Spectrosc. 30:899–912 [Google Scholar]
  25. Ferrari AC, Meyer JC, Scardaci V, Casiraghi C, Lazzeri M. 25.  et al. 2006. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97:187401 [Google Scholar]
  26. Malard LM, Pimenta MA, Dresselhaus G, Dresselhaus MS. 26.  2009. Raman spectroscopy in graphene. Phys. Rep. 473:51–87 [Google Scholar]
  27. Zabel J, Nair RR, Ott A, Georgiou T, Geim AK. 27.  et al. 2011. Raman spectroscopy of graphene and bilayer under biaxial strain: bubbles and balloons. Nano Lett. 12:617–21 [Google Scholar]
  28. Lee J-U, Yoon D, Cheong H. 28.  2012. Estimation of Young's modulus of graphene by Raman spectroscopy. Nano Lett. 12:4444–48 [Google Scholar]
  29. Ding F, Ji H, Chen Y, Herklotz A, Dörr K. 29.  et al. 2010. Stretchable graphene: a close look at fundamental parameters through biaxial straining. Nano Lett. 10:3453–58 [Google Scholar]
  30. Filintoglou K, Papadopoulos N, Arvanitidis J, Christofilos D, Frank O. 30.  et al. 2013. Raman spectroscopy of graphene at high pressure: effects of the substrate and the pressure transmitting media. Phys. Rev. B 88:045418 [Google Scholar]
  31. Nicolle J, Machon D, Poncharal P, Pierre-Louis O, San-Miguel A. 31.  2011. Pressure-mediated doping in graphene. Nano Lett. 11:3564–68 [Google Scholar]
  32. Proctor JE, Gregoryanz E, Novoselov KS, Lotya M, Coleman JN, Halsall MP. 32.  2009. High-pressure Raman spectroscopy of graphene. Phys. Rev. B 80:073408–4 [Google Scholar]
  33. Ni ZH, Yu T, Lu YH, Wang YY, Feng YP, Shen ZX. 33.  2008. Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening. ACS Nano 2:2301–5 [Google Scholar]
  34. Huang MY, Yan HG, Chen CY, Song DH, Heinz TF, Hone J. 34.  2009. Phonon softening and crystallographic orientation of strained graphene studied by Raman spectroscopy. PNAS 106:7304–8 [Google Scholar]
  35. Frank O, Mohr M, Maultzsch J, Thomsen C, Riaz I. 35.  et al. 2011. Raman 2D-band splitting in graphene: theory and experiment. ACS Nano 5:2231–39 [Google Scholar]
  36. Frank O, Tsoukleri G, Riaz I, Papagelis K, Parthenios J. 36.  et al. 2011. Development of a universal stress sensor for graphene and carbon fibres. Nat. Commun. 2:255 [Google Scholar]
  37. Mohr M, Papagelis K, Maultzsch J, Thomsen C. 37.  2009. Two-dimensional electronic and vibrational band structure of uniaxially strained graphene from ab initio calculations. Phys. Rev. B 80:205410 [Google Scholar]
  38. Yoon D, Son Y-W, Cheong H. 38.  2011. Strain-dependent splitting of the double-resonance Raman scattering band in graphene. Phys. Rev. Lett. 106:155502 [Google Scholar]
  39. Gong L, Kinloch IA, Young RJ, Riaz I, Jalil R, Novoselov KS. 39.  2010. Interfacial stress transfer in a graphene monolayer nanocomposite. Adv. Mater. 22:2694–97 [Google Scholar]
  40. Gong L, Young RJ, Kinloch IA, Riaz I, Jalil R, Novoselov KS. 40.  2012. Optimizing the reinforcement of polymer-based nanocomposites by graphene. ACS Nano 6:2086–95 [Google Scholar]
  41. Young RJ, Gong L, Kinloch IA, Riaz I, Jalil R, Novoselov KS. 41.  2011. Strain mapping in a graphene monolayer nanocomposite. ACS Nano 5:3079–84 [Google Scholar]
  42. Young RJ, Kinloch IA, Gong L, Novoselov KS. 42.  2012. The mechanics of graphene nanocomposites: a review. Compos. Sci. Technol. 72:1459–76 [Google Scholar]
  43. Frank O, Bouša M, Riaz I, Jalil R, Novoselov KS. 43.  et al. 2012. Phonon and structural changes in deformed bernal stacked bilayer graphene. Nano Lett. 12:687–93 [Google Scholar]
  44. Huang M, Yan H, Heinz TF, Hone J. 44.  2010. Probing strain-induced electronic structure change in graphene by Raman spectroscopy. Nano Lett. 10:4074–79 [Google Scholar]
  45. Mohr M, Maultzsch J, Thomsen C. 45.  2010. Splitting of the Raman 2D band of graphene subjected to strain. Phys. Rev. B 82:201409(R) [Google Scholar]
  46. Narula R, Bonini N, Marzari N, Reich S. 46.  2012. Dominant phonon wave vectors and strain-induced splitting of the 2D Raman mode of graphene. Phys. Rev. B 85:115451 [Google Scholar]
  47. Popov VN, Lambin P. 47.  2013. Theoretical 2D Raman band of strained graphene. Phys. Rev. B 87:155425 [Google Scholar]
  48. Heeg S, Fernandez-Garcia R, Oikonomou A, Schedin F, Narula R. 48.  et al. 2013. Polarized plasmonic enhancement by Au nanostructures probed through Raman scattering of suspended graphene. Nano Lett. 13:301–8 [Google Scholar]
  49. Heeg S, Oikonomou A, Garcia RF, Maier SA, Vijayaraghavan A, Reich S. 49.  2013. Strained graphene as a local probe for plasmon-enhanced Raman scattering by gold nanostructures. Phys. Status Solidi RRL 7:1067–70 [Google Scholar]
  50. Gong L, Young RJ, Kinloch IA, Haigh SJ, Warner JH. 50.  et al. 2013. Reversible loss of Bernal stacking during the deformation of few-layer graphene in nanocomposites. ACS Nano 7:7287–94 [Google Scholar]
  51. 51.  Deleted in proof
  52. Pérez Garza HH, Kievit EW, Schneider GF, Staufer U. 52.  2014. Controlled, reversible, and nondestructive generation of uniaxial extreme strains (>10%) in graphene. Nano Lett. 14:4107–13 [Google Scholar]
  53. Bissett MA, Izumida W, Saito R, Ago H. 53.  2012. Effect of domain boundaries on the Raman spectra of mechanically strained graphene. ACS Nano 6:10229–38 [Google Scholar]
  54. Jegal S, Hao Y, Yoon D, Ruoff RS, Yun H. 54.  et al. 2013. Crystallographic orientation of early domains in CVD graphene studied by Raman spectroscopy. Chem. Phys. Lett. 568–69:146–50 [Google Scholar]
  55. Raju APA, Lewis A, Derby B, Young RJ, Kinloch IA. 55.  et al. 2014. Wide-area strain sensors based upon graphene-polymer composite coatings probed by Raman spectroscopy. Adv. Funct. Mater. 24:2865–74 [Google Scholar]
  56. Sfyris D, Galiotis C. 56.  2014. Curvature-dependent surface energy for free-standing monolayer graphene. Math. Mech. Sol. In press. doi:10.1177/1081286514537667
  57. Sfyris D, Sfyris GI, Galiotis C. 57.  2014. Curvature dependent surface energy for a free standing monolayer graphene: Some closed form solutions of the non-linear theory. Int. J. Non-Linear Mech. 67:186–97 [Google Scholar]
  58. Sfyris D, Sfyris GI, Galiotis C. 58.  2014. Curvature dependent surface energy for free standing monolayer graphene: geometrical and material linearization with closed form solutions. Int. J. Eng. Sci. 85:224–33 [Google Scholar]
  59. Wei Y, Wang B, Wu J, Yang R, Dunn ML. 59.  2012. Bending rigidity and Gaussian bending stiffness of single-layered graphene. Nano Lett. 13:26–30 [Google Scholar]
  60. Lu Q, Huang R. 60.  2009. Nonlinear mechanics of single-atomic-layer graphene sheets. Int. J. Appl. Mech. 01:443–67 [Google Scholar]
  61. Zhou J, Huang R. 61.  2008. Internal lattice relaxation of single-layer graphene under in-plane deformation. J. Mech. Phys. Sol. 56:1609–23 [Google Scholar]
  62. Tapasztó L, Dumitrică T, Kim SJ, Nemes-Incze P, Hwang C, Biró LP. 62.  2012. Breakdown of continuum mechanics for nanometre-wavelength rippling of graphene. Nat. Phys. 8:739–42 [Google Scholar]
  63. Steigmann DJ. 63.  2012. A well-posed finite-strain model for thin elastic sheets with bending stiffness. Math. Mech. Sol. 18:103–12 [Google Scholar]
  64. Friesecke G, James RD, Müller S. 64.  2006. A hierarchy of plate models derived from nonlinear elasticity by gamma-convergence. Arch. Ration. Mech. Anal. 180:183–236 [Google Scholar]
  65. Arroyo M, Belytschko T. 65.  2002. An atomistic-based finite deformation membrane for single layer crystalline films. J. Mech. Phys. Sol. 50:1941–77 [Google Scholar]
  66. Davini C. 66.  2014. Homogenization of a graphene sheet. Contin. Mech. Thermodyn. 26:95–113 [Google Scholar]
  67. Caillerie D, Mourad A, Raoult A. 67.  2006. Discrete homogenization in graphene sheet modeling. J. Elast. 84:33–68 [Google Scholar]
  68. Arash B, Wang Q. 68.  2012. A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes. Comput. Mater. Sci. 51:303–13 [Google Scholar]
  69. Jomehzadeh E, Afshar MK, Galiotis C, Shi X, Pugno NM. 69.  2013. Nonlinear softening and hardening nonlocal bending stiffness of an initially curved monolayer graphene. Int. J. Non-Linear Mech. 56:123–31 [Google Scholar]
  70. Warner JH, Margine ER, Mukai M, Robertson AW, Giustino F, Kirkland AI. 70.  2012. Dislocation-driven deformations in graphene. Science 337:209–12 [Google Scholar]
  71. Ariza MP, Ortiz M. 71.  2010. Discrete dislocations in graphene. J. Mech. Phys. Sol. 58:710–34 [Google Scholar]
  72. Dettori R, Cadelano E, Colombo L. 72.  2012. Elastic fields and moduli in defected graphene. J. Phys. Condens. Matter 24:104020 [Google Scholar]
  73. Carpio A, Bonilla LL, de Juan F, Vozmediano MAH. 73.  2008. Dislocations in graphene. New J. Phys. 10:053021 [Google Scholar]
  74. Zhang Z, Yang Y, Yakobson BI. 74.  2014. Grain boundaries in hybrid two-dimensional materials. J. Mech. Phys. Sol. 70:62–70 [Google Scholar]
  75. Li XL, Wang XR, Zhang L, Lee SW, Dai HJ. 75.  2008. Chemically derived, ultrasmooth graphene nanoribbon semiconductors. Science 319:1229–32 [Google Scholar]
  76. Niyogi S, Bekyarova E, Itkis ME, Zhang H, Shepperd K. 76.  et al. 2010. Spectroscopy of covalently functionalized graphene. Nano Lett. 10:4061–66 [Google Scholar]
  77. Levy N, Burke SA, Meaker KL, Panlasigui M, Zettl A. 77.  et al. 2010. Strain-induced pseudo–magnetic fields greater than 300 tesla in graphene nanobubbles. Science 329:544–47 [Google Scholar]
  78. Bissett MA, Tsuji M, Ago H. 78.  2014. Strain engineering the properties of graphene and other two-dimensional crystals. Phys. Chem. Chem. Phys. 16:11124–38 [Google Scholar]
  79. Ohta T, Bostwick A, Seyller T, Horn K, Rotenberg E. 79.  2006. Controlling the electronic structure of bilayer graphene. Science 313:951–54 [Google Scholar]
  80. 80.  Deleted in proof
  81. Pereira VM, Castro Neto AH, Peres NMR. 81.  2009. Tight-binding approach to uniaxial strain in graphene. Phys. Rev. B 80:045401 [Google Scholar]
  82. Ribeiro RM, Pereira VM, Peres NMR, Briddon PR, Neto AHC. 82.  2009. Strained graphene: tight-binding and density functional calculations. New J. Phys. 11:115002 [Google Scholar]
  83. Gui G, Li J, Zhong J. 82a.  2009. Reply to “Comment on ‘Band structure engineering of graphene by strain: first-principles calculations.’”. Phys. Rev. B 80:167402 [Google Scholar]
  84. Farjam M, Rafii-Tabar H. 83.  2009. Comment on “Band structure engineering of graphene by strain: first-principles calculations.”. Phys. Rev. B 80:167401 [Google Scholar]
  85. Choi S-M, Jhi S-H, Son Y-W. 84.  2010. Effects of strain on electronic properties of graphene. Phys. Rev. B 81:081407 [Google Scholar]
  86. Ni ZH, Yu T, Lu YH, Wang YY, Feng YP, Shen ZX. 85.  2008. Uniaxial strain on graphene: Raman spectroscopy study and band-gap opening. ACS Nano 2:112301–5 [Google Scholar]
  87. Bissett MA, Konabe S, Okada S, Tsuji M, Ago H. 86.  2013. Enhanced chemical reactivity of graphene induced by mechanical strain. ACS Nano 7:10335–43 [Google Scholar]
  88. Wu Q, Wu Y, Hao Y, Geng J, Charlton M. 87.  et al. 2013. Selective surface functionalization at regions of high local curvature in graphene. Chem. Commun. 49:677–79 [Google Scholar]
  89. Kim KS, Zhao Y, Jang H, Lee SY, Kim JM. 88.  et al. 2009. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 457:706–10 [Google Scholar]
  90. Cocco G, Cadelano E, Colombo L. 89.  2010. Gap opening in graphene by shear strain. Phys. Rev. B 81:241412 [Google Scholar]
  91. Lee SH, Chiu CW, Ho YH, Lin MF. 90.  2010. Uniaxial-stress effects on electronic structures of monolayer and bilayer graphenes. Synth. Met. 160:2435–41 [Google Scholar]
  92. Nanda BRK, Satpathy S. 91.  2009. Strain and electric field modulation of the electronic structure of bilayer graphene. Phys. Rev. B 80:165430 [Google Scholar]
  93. Verberck B, Partoens B, Peeters FM, Trauzettel B. 92.  2012. Strain-induced band gaps in bilayer graphene. Phys. Rev. B 85:125403 [Google Scholar]
  94. Choi S-M, Jhi S-H, Son Y-W. 93.  2010. Controlling energy gap of bilayer graphene by strain. Nano Lett. 10:3486–89 [Google Scholar]
  95. Mucha-Kruczynski M, Aleiner IL, Fal'ko VI. 94.  2011. Strained bilayer graphene: band structure topology and Landau level spectrum. Phys. Rev. B 84:041404 [Google Scholar]
  96. Wong J-H, Wu B-R, Lin M-F. 95.  2012. Strain effect on the electronic properties of single layer and bilayer graphene. J. Phys. Chem. C 116:8271–77 [Google Scholar]
  97. Malard LM, Elias DC, Alves ES, Pimenta MA. 96.  2008. Observation of distinct electron-phonon couplings in gated bilayer graphene. Phys. Rev. Lett. 101:257401 [Google Scholar]
  98. Guinea F, Katsnelson MI, Geim AK. 97.  2010. Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering. Nat. Phys. 6:30–33 [Google Scholar]
  99. Low T, Guinea F. 98.  2010. Strain-induced pseudomagnetic field for novel graphene electronics. Nano Lett. 10:3551–54 [Google Scholar]
  100. Drost R, Uppstu A, Schulz F, Hämäläinen SK, Ervasti M. 99.  et al. 2014. Electronic states at the graphene–hexagonal boron nitride zigzag interface. Nano Lett. 14:5128–32 [Google Scholar]

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error