In the present study, the method of asymptotic ho-mogenization is used to estimate elastic properties as well as tension, bending and twisting rigidities of single-layer graphene sheets (SLGSs). To this end, asymptotic homoge-nization of a reinforced composite is developed for modeling of SLGS by assuming that the covalent bond be-tween carbon atoms can be represented by reinforcements. Applicable formulas are obtained for the elastic properties and rigidities of SLGS directly from the interatomic interac-tions 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 dif-ferent 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 nanocomposites and other nanostructures.

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