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 Föppl-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 Föppl-von Karman theory and provide quantitative estimates for the different regimes.The truth about the cat in a graphene hammockMechanical properties of graphene are important for both everyday and exotic applications, from sensors and resonators to graphene sails for interstellar travels. Textbook elasticity theory that all engineers learn and use is not applicable to atomic layers like graphene because of the crucial effect of thermal fluctuations. As a result, the Young modulus and other elastic constants of graphene are not fixed parameters of the material but strongly dependent on temperature, size and external load. Based on atomistic simulations, a group at Radboud University in The Netherlands has developed a quantitative theory of the mechanics of graphene. In particular, a one squared meter hammock made of graphene could sustain a cat weighing about three kilograms at room temperature. The derived scaling laws apply to all two-dimensional materials.