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

Abstract

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.

References in corpus (8)

• Finite temperature lattice properties of graphene beyond the quasiharmonic approximation
• Nonlinear elasticity of monolayer graphene
• Curvature dependent surface energy for a free standing monolayer graphene: some closed form solutions of the nonlinear theory
• Curvature dependent surface energy for free standing monolayer graphene: geometrical and material linearization with closed form solutions
• The Gaussian Stiffness of Graphene deduced from a Continuum Model based on Molecular Dynamics Potentials
• A 2D metamaterial with auxetic out-of-plane behavior and non-auxetic in-plane behavior
• An analytical benchmark for MD codes: testing LAMMPS on the 2nd generation Brenner potential
• A new material property of graphene: the bending Poisson coefficient