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In this study, by modeling van der Waals (vdWs) interactions based on the Lennard-Jones potential function interlayer tensile-compressive and shear moduli of bilayer graphene sheets are analytically calculated. To this end, by varying potential depth parameter which shows the strength of vdWs interactions a new model is presented for calculating interlayer in-plane and out-of-plane moduli for two different stacking patterns. In order to determine the interlayer vdWs moduli, a small flake of monolayer graphene is sliding on a large monolayer graphene substrate and accordingly variations of vdWs forces as well as the interlayer shear and normal strains are recorded. The relative displacements of layers cause linear strain and stress. In the model, bilayer graphene geometry (being armchair or zigzag, and stacking pattern) and potential depth parameter are two important parameters for determination of vdWs moduli. The accuracy of the method is verified by comparing the present results with those reported in literatures. Finally, close-form relations for interlayer tensile-compressive and shear moduli of vdWs interactions versus the depth potential parameter are presented for ABA and AAA stacking patterns as well as zigzag and armchair directions. It is observed that the interlayer moduli have linear relation with the potential depth parameter.

Keywords: Geometrical-analytical method, Bilayer graphene, Van der Waals interactions, Shear modulus, Tensile-compressive modulus

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