A REBO-potential-based model for graphene bending by Gamma-convergence

An atomistic to continuum model for a graphene sheet undergoing bending is presented. Under the assumption that the atomic interactions are governed by a harmonic approximation of the 2nd-generation Brenner REBO (reactive empirical bond-order) potential, involving first, second and third nearest neighbors of any given atom, we determine the variational limit of the energy functionals. It turns out that the $\Gamma$-limit depends on the linearized mean and Gaussian curvatures. If some specific contributions in the atomic interaction are neglected, the variational limit is non-local.