Graphene deposited on planar surfaces often exhibits sharp and localized folds delimiting seemingly planar regions, as a result of compressive stresses transmitted by the substrate. Such folds alter the electronic and chemical properties of graphene, and therefore, it is important to understand their emergence, to either suppress them or control their morphology. Here, we study the emergence of out-of-plane deformations in supported and laterally strained graphene with high-fidelity simulations and a simpler theoretical model. We characterize the onset of buckling and the nonlinear behavior after the instability in terms of the adhesion and frictional material parameters of the graphene-substrate interface. We find that localized folds evolve from a distributed wrinkling linear instability due to the nonlinearity in the van der Waals graphene-substrate interactions. We identify friction as a selection mechanism for the separation between folds, as the formation of far apart folds is penalized by the work of friction. Our systematic analysis is a first step towards strain engineering of supported graphene, and is applicable to other compressed thin elastic films weakly coupled to a substrate.
Bibliographical noteFunding Information:
We acknowledge the support of the European Research Council under the European Community's 7th Framework Programme (FP7/2007-2013)/ERC Grant Agreement No. 240487. K.Z. acknowledges the support of the UPC. M.A. acknowledges the support received through the prize “ICREA Academia” for excellence in research, funded by the Generalitat de Catalunya.