Scaling Behavior and Strain Dependence of In-Plane Elastic Properties of Graphene

We show by atomistic simulations that, in the thermodynamic limit, the in-plane elastic moduli of graphene at finite temperature vanish with system size L as a power law L-eta u with eta(u) similar or equal to 0.325, in agreement with the membrane theory. We provide explicit expressions for the size and strain dependence of graphene's elastic moduli, allowing comparison to experimental data. Our results explain the recently experimentally observed increase of the Young modulus by more than a factor of 2 for a tensile strain of only a few per mill. The difference of a factor of 2 between the measured asymptotic value of the Young modulus for tensilely strained systems and the value from ab initio calculations remains, however, unsolved. We also discuss the asymptotic behavior of the Poisson ratio, for which our simulations disagree with the predictions of the self-consistent screening approximation.