An atomistic-based Föppl–von Kármán model for graphene. (November 2019)

• Record Type: Journal Article
• Authors: Davini, Cesare; Favata, Antonino; Paroni, Roberto
• Is Part Of: International journal of non-linear mechanics. Volume 116(2019)
• Page Start: 281
• Page End: 288
• Publication Date: 2019-11
• Subjects: Graphene -- Continuum modeling -- Föppl–von Kármán equations; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.07.011
• Languages: English
• ISSNs: 0020-7462

Abstract

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.