A method that utilises atomic trajectories and velocities from molecular dynamics simulations has been suitably adapted and employed for the implicit calculation of the phonon dispersion curves of graphene. Classical potentials widely used in the literature were employed. Their performance was assessed for each individual phonon branch and the overall phonon dispersion, using available inelastic x-ray scattering data. The method is promising for systems with large scale periodicity, accounts for anharmonic effects and non-bonding interactions with a general environment and it is applicable under finite temperatures. The temperature dependence of the phonon dispersion curves has been examined with emphasis on the doubly degenerate Raman active Γ-E_2g phonon at the zone centre, where experimental results are available. The potentials used show diverse behaviour. The Tersoff-2010 potential exhibits the most systematic and physically sound behaviour in this regard and gives a first-order temperature coefficient of χ = −0.05 cm⁻¹/K for the Γ-E_2g shift in agreement with reported experimental values.

Achieving structural superlubricity in graphitic samples of macroscale size is particularly challenging due to difficulties in sliding large contact areas of commensurate stacking domains. Here, we show the presence of macroscale structural superlubricity between two randomly stacked graphene layers produced by both mechanical exfoliation and chemical vapour deposition. By measuring the shifts of Raman peaks under strain we estimate the values of frictional interlayer shear stress (ILSS) in the superlubricity regime (mm scale) under ambient conditions. The random incommensurate stacking, the presence of wrinkles and the mismatch in the lattice constant between two graphene layers induced by the tensile strain differential are considered responsible for the facile shearing at the macroscale. Furthermore, molecular dynamic simulations show that the stick-slip behaviour does not hold for incommensurate chiral shearing directions for which the ILSS decreases substantially, supporting the experimental observations. Our results pave the way for overcoming several limitations in achieving macroscale superlubricity using graphene.

The stress transfer mechanism from a polymer substrate to a nanoinclusion, such as a graphene flake, is of extreme interest for the production of effective nanocomposites. Previous work conducted mainly at the micron scale has shown that the intrinsic mechanism of stress transfer is shear at the interface. However, since the interfacial shear takes its maximum value at the very edge of the nanoinclusion it is of extreme interest to assess the effect of edge integrity upon axial stress transfer at the submicron scale. Here, we conduct a detailed Raman line mapping near the edges of a monolayer graphene flake that is simply supported onto an epoxy-based photoresist (SU8)/poly(methyl methacrylate) matrix at steps as small as 100 nm. We show for the first time that the distribution of axial strain (stress) along the flake deviates somewhat from the classical shear-lag prediction for a region of ∼2 μm from the edge. This behavior is mainly attributed to the presence of residual stresses, unintentional doping, and/or edge effects (deviation from the equilibrium values of bond lengths and angles, as well as different edge chiralities). By considering a simple balance of shear-to-normal stresses at the interface we are able to directly convert the strain (stress) gradient to values of interfacial shear stress for all the applied tensile levels without assuming classical shear-lag behavior. For large flakes a maximum value of interfacial shear stress of 0.4 MPa is obtained prior to flake slipping.

Thin membranes, such as monolayer graphene of monoatomic thickness, are bound to exhibit lateral buckling under uniaxial tensile loading that impairs its mechanical behaviour. In this work, we have developed an experimental device to subject 2D materials to controlled equibiaxial strain on supported beams that can be flexed up or down to subject the material to either compression or tension, respectively. Using strain gauges in tandem with Raman spectroscopy measurements, we monitor the G and 2D phonon properties of graphene under biaxial strain and thus extract important information about the uptake of stress under these conditions. The experimental shift over strain for the G and 2D Raman peaks were found to be in the range of 62.3 ± 5 cm^–1/% and 148.2 ± 6 cm^–1/%, respectively, for monolayer but also bilayer graphenes. The corresponding Grüneisen parameters for the G and 2D peaks were found to be between 1.97 ± 0.15 and 2.86 ± 0.12, respectively. These values agree reasonably well with those obtained from small-strain bubble-type experiments. The results presented are also backed up by classical and ab initio molecular dynamics simulations and excellent agreement of Γ-E_2g shifts with strains and the Grüneisen parameter was observed.

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.