An atomistic-based Föppl–von Kármán model for graphene. (November 2019) - Davini, Cesare; Favata, Antonino; Paroni, Roberto
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 Föppl–von Kármán type, whose constitutive coefficients are given in terms of the atomistic interactions. Highlights: A discrete model accounting for third-neighbor interaction in the description of the atomistic energy of graphene. An homogenization procedure that leads to a simple continuum model. Accounting for relatively large out-of-plane displacements. Identification of the continuum stiffness parameters in terms of the atomistic interactions.