  The mechanical behavior of graphitic materials is greatly affected by the
weak interlayer bonding with van der Waals forces for a range of thickness from
nano to macroscale. Herein, we present a comprehensive study of the effect of
layer thickness on the compression behavior of graphitic materials such as
graphene which are fully embedded in polymer matrices. Raman Spectroscopy was
employed to identify experimentally the critical strain to failure of the
graphitic specimens. The most striking finding is that, contrary to what would
be expected from Eulerian mechanics, the critical compressive strain to failure
decreases with increase of flake thickness. This is due to the layered
structure of the material and in particular the weak cohesive forces that hold
the layers together. The plate phenomenology breaks down for the case of
multi-layer graphene, which can be approached as discrete single layers weakly
bonded to each other. This behavior is modelled here by considering the
interlayer bonding (van der Waals forces) as springs in series, and very good
agreement was found between theory and experiment. Finally, it will be shown
that in the post failure regime multi-layer graphenes exhibit negative
stiffness and thus behave as mechanical metamaterials.
