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 framework. 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 the 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.