  Polycrystalline graphene has an inherent tendency to buckle, i.e. develop
out-of-plane, three-dimensional structure. A force applied to stretch a piece
of polycrystalline graphene influences the out-of-plane structure. Even if the
graphene is well-relaxed, this happens in non-linear fashion: occasionally, a
tiny increase in stretching force induces a significant displacement, in close
analogy to avalanches, which in turn can create vibrations in the surrounding
medium. We establish this effect in computer simulations: by continuously
changing the strain, we follow the displacements of the carbon atoms that turn
out to exhibit a discontinuous evolution. Furthermore, the displacements
exhibit a hysteretic behavior upon the change from low to high stress and back.
These behaviors open up a new direction in studying dynamical elasticity of
polycrystalline quasi-two-dimensional systems, and in particular the
implications on their mechanical and thermal properties.
