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 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.
A REBO-Potential-Based Model for Graphene Bending by Γ -Convergence
Paroni, Roberto
2018-01-01
Abstract
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 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.File in questo prodotto:
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