A new material property of graphene: the bending Poisson coefficient

The in-plane infinitesimal deformations of graphene are well understood: they can be computed by solving the equilibrium problem for a sheet of isotropic elastic material with suitable stretching stiffness and Poisson coefficient $\nu^{(m)}$. Here, we pose the following question: does the Poisson coefficient $\nu^{(m)}$ affect the response to bending of graphene? Despite what happens if one adopts classical structural models, it does not. In this letter we show that a new material property, conceptually and quantitatively different from $\nu^{(m)}$, has to be introduced. We term this new parameter bending Poisson coefficient; we propose for it a physical interpretation in terms of the atomic interactions and produce a quantitative evaluation.