Evaluation of Tension, Bending and Twisting Rigidities of Single-Layer Graphene Sheets by an Analytical Asymptotic Homogenization Model

Abstract

In the present study, the method of asymptotic homogenization is used to estimate elastic properties as well as tension, bending and twisting rigidities of single-layer graphene sheets (SLGSs). To this end, asymptotic homogenization of a reinforced composite is developed for modeling of SLGS by assuming that the covalent bond between carbon atoms can be represented by reinforcements. Applicable formulas are obtained for the elastic properties and rigidities of SLGS directly from the interatomic interactions through three types of potentials. It is proved that force field constants significantly affect the elastic properties of SLGS. Herein, the elastic moduli are obtained based on different types of atomic force constants. The results of the present analytical model are in close agreements with the similar theoretical results and experimental measurements. This approach can be developed to represent mechanical properties of nanotubes, nanocomposites and other nanostructures.

DOI: http://dx.doi.org/10.5755/j01.mech.24.2.17822