The influence of strain on the elastic constants of graphene

Recent advances in the understanding of graphene elasticity have shown that suspended graphene does not behave as a conventional thin plate but has a more complex behavior where flexural modes play a significant role. Among other effects, out-of-plane thermal fluctuations modify the in-plane elastic properties. Here we report indentation experiments on graphene subjected to strain. This strain is achieved by applying pressure difference across suspended graphene drumheads. Our indentation curves show an increased mechanical response at strains larger than 0.3%. Finite element simulations of the indentation curves on pressurized membranes show that this observation can be ascribed to a twofold increase of the in-plane elastic modulus and the Poisson ratio. Based in the thermodynamic theory of elastic membranes, this increase is attributed to the suppression of out-of-plane fluctuations by strain. This result reinforces the idea that suspended graphene behaves as a fluctuating membrane and points out that a careful analysis should be done when analyzing indentation curves on atomic thick materials.