Mechanics of thermally fluctuating membranes

Besides having unique electronic properties, graphene is claimed to be the strongest material in nature due to its Young modulus, which is, per atomic layer, much larger than that of steel. This reasoning however does not take into account the peculiar properties of graphene as a thermally fluctuating crystalline membrane, which at finite temperature, lead to a dramatic reduction of the Young modulus for micron-sized graphene samples in comparison with atomic scale values. We show that the standard Fppl-von Karman elasticity theory for thin plates, routinely used for the interpretation of experimental results has to be modified for graphene at room temperature and for micron-sized samples. Based on scaling analysis and atomistic simulation, we investigate the mechanics of graphene under transverse load up to breaking. We determine the limits of applicability of the Fppl-von Karman theory and provide quantitative estimates for the different regimes.