  Central to most applications involving monolayer graphene is its mechanical
response under various stress states. To date most of the work reported is of
theoretical nature and refers to tension and compression loading of model
graphene. Most of the experimental work is indeed limited to bending of single
flakes in air and the stretching of flakes up to typically ~1% using plastic
substrates. Recently we have shown that by employing a cantilever beam we can
subject single graphene into various degrees of axial compression. Here we
extend this work much further by measuring in detail both stress uptake and
compression buckling strain in single flakes of different geometries. In all
cases the mechanical response is monitored by simultaneous Raman measurements
through the shift of either the G or 2D phonons of graphene. In spite of the
infinitely small thickness of the monolayers, the results show that graphene
embedded in plastic beams exhibit remarkable compression buckling strains. For
large length (l)-to-width (w) ratios (> 0.2) the buckling strain is of the
order of -0.5% to -0.6%. However, for l/w <0.2 no failure is observed for
strains even higher than -1%. Calculations based on classical Euler analysis
show that the buckling strain enhancement provided by the polymer lateral
support is more than six orders of magnitude compared to suspended graphene in
air.
