Continual model of deformation of graphene

Abstract

A single-layered graphene sheet is investigated. It is accepted that the total potential energy of the system under consideration consists of four parts. The first of them is the bond stretching energy describing interaction between two neighbouring atoms (the Morse potential). The second is the in-plane angle bending energy depending on the position of three neighbouring atoms (the Brenner’s potential). The third is the energy of the atom deflection out of the plane of three neighbouring atoms. And the fourth is the torsion energy of four neighbouring atoms. The Van-der-Waals forces are neglected. Only the small deflections are studied. By using the long-waves approximation the continuous stretching and bending 2D energy density is delivered. As a result, the equivalent plate with the elastic stretching and bending modules is obtained. The natural frequencies of a rectangular plate are found. The stability under the in- plane compression is investigated. For this aim the nonlinear terms depending on the transversal deflection are included in the tangential stresses. The numerical results are compared with the results of the other authors obtained by the molecular dynamics method. Refs 16. Figs 1.

Keywords:

graphen, stiffness, vibrations, stability