Archive for Rational Mechanics and Analysis

, Volume 229, Issue 3, pp 1153–1195 | Cite as

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.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.UdineItaly
  2. 2.Department of Structural and Geotechnical EngineeringSapienza University of RomeRomeItaly
  3. 3.Dipartimento di Ingegneria Civile e IndustrialeUniversità di PisaPisaItaly

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