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

We present an atomistic to continuum model for a graphene sheet undergoing bending, within the small displacements approximation frame- work. Under the assumption that the atomic interactions are governed by a harmonic approximation of the 2nd-generation Brenner REBO (reactive em- pirical bond-order) potential, involving first, second and third nearest neigh- bors of any given atom, we determine the variational limit of the energy func- tionals. It turns out that the Γ-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.