Exfoliated monolayer graphene flakes were embedded in a polymer matrix and loaded under axial compression. By monitoring the shifts of the 2D Raman phonons of rectangular flakes of various sizes under load, the critical strain to failure was determined. Prior to loading care was taken for the examined area of the flake to be free of residual stresses. The critical strain values for first failure were found to be independent of flake size at a mean value of –0.60% corresponding to a yield stress up to -6 GPa. By combining Euler mechanics with a Winkler approach, we show that unlike buckling in air, the presence of the polymer constraint results in graphene buckling at a fixed value of strain with an estimated wrinkle wavelength of the order of 1–2 nm. These results were compared with DFT computations performed on analogue coronene/PMMA oligomers and a reasonable agreement was obtained.

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.

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The purpose of the present work is to give a continuum model that can capture bending effects for free-standing graphene monolayers taking material’s symmetry properly into account. Starting from the discrete picture of graphene modelled as a hexagonal 2-lattice, we give the arithmetic symmetries. Confined to weak transformation neighbourhoods one is able to work with the geometric symmetry group. Use of the Cauchy–Born rule allows the transition from the discrete case to the continuum case. At the continuum level we use a surface energy that depends on an in-plane strain measure, the curvature tensor and the shift vector. Dependence of the energy on the curvature tensor allows for incorporating bending effects into the model. Dependence on the shift vector is motivated by the fact that discretely graphene is a 2-lattice. We lay down the complete and irreducible set of invariants for this surface energy amenable to available representation theory. This way we obtain the expression for the surface stress as well as the surface couple stress tensor, the first being responsible for the in-plane deformations and the second for the out-of-plane motions. Forms for the elasticities of the material are given accompanied by the field equations. The model, in its simplest form, predicts 13 independent scalar variables in the constitutive relations to be observed in experiments. The framework presented is valid for both materially and geometrically nonlinear theories. We also present the case where symmetry changes at the continuum level, without taking into account how energy behaves at the transition regime.

Continuum modeling of a free-standing graphene monolayer, viewed as a two dimensional 2-lattice, requires specifications of the components of the shift vector that act as an auxiliary variable. The field equations are then the equations ruling the shift vector, together with momentum and moment of momentum equations. We present an analysis of simple loading histories such as axial, biaxial tension/compression and simple shear for a range of problems of increasing difficulty. We start by laying down the equations of a simplified model which can still capture bending effects. Initially, we ignore out of plane deformations. For this case, we solve analytically the equations ruling the auxiliary variables in terms of the shift vector; these equations are algebraic when the loading is specified. As a next step, still working on the simplified model, out-of-plane deformations are taken into account and the equations complicate dramatically. We describe how wrinkling/buckling can be introduced into the model and apply the Cauchy-Kowalevski theorem to get existence and uniqueness in terms of the shift vector for some characteristic cases. Finally, for the treatment of the most general problem, we classify the equations of momentum and give conditions for the Cauchy-Kowalevski theorem to apply.