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arXiv · 1902.10702

An atomistic-based F\"oppl-von K\'arm\'an model for graphene

Cesare Davini·Antonino Favata·Roberto Paroni
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Abstract

We deduce a non-linear continuum model of graphene for the case of finite out-of-plane displacements and small in-plane deformations. On assuming that the lattice interactions are governed by the Brenner's REBO potential of 2nd generation and that self-stress is present, we introduce discrete strain measures accounting for up-to-the-third neighbor interactions. The continuum limit turns out to depend on an average (macroscopic) displacement field and a relative shift displacement of the two Bravais lattices that give rise to the hexagonal periodicity. On minimizing the energy with respect to the shift variable, we formally determine a continuum model of F\"oppl-von K\'arm\'a type, whose constitutive coefficients are given in terms of the atomistic interactions.

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Cesare Davini, Antonino Favata, Roberto Paroni. 2019-02-27. An atomistic-based F\"oppl-von K\'arm\'an model for graphene. https://arxiv.org/abs/1902.10702

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