  Besides having unique electronic properties, graphene is claimed to be the
strongest material in nature. In the press release of the Nobel committee it is
claimed that a hammock made of a squared meter of one-atom thick graphene could
sustain the wight of a 4 kg cat. More practically important are applications of
graphene like scaffolds and sensors which are crucially dependent on the
mechanical strength. Meter-sized graphene is even being considered for the
lightsails in the starshot project to reach the star alpha centaury. The
predicted strength of graphene is based on its very large Young modulus which
is, per atomic layer, much larger than that of steel. This reasoning however
would apply to conventional thin plates but does not take into account the
peculiar properties of graphene as a thermally fluctuating crystalline
membrane. It was shown recently both experimentally and theoretically that
thermal fluctuations lead to a dramatic reduction of the Young modulus and
increase of the bending rigidity for micron-sized graphene samples in
comparison with atomic scale values. This makes the use of the standard
F\"oppl-von Karman elasticity (FvK) theory for thin plates not directly
applicable to graphene and other single atomic layer membranes. This fact is
important because the current interpretation of experimental results is based
on the FvK theory. In particular, we show that the FvK-derived Schwerin
equation, routinely used to derive the Young modulus from indentation
experiments has to be essentially 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 FvK theory and provide
quantitative estimates for the different regimes.
