On the derivation of the elastic properties of lattice nanostructure: The case of graphene sheets

Several nanomechanics approaches based on common two or three-body potentials are compared. Numerical simulations and analytical approaches are used to investigate the not negligible differences among the prediction of the in-plane elastic constants of graphene sheets in the literature, exploring separately the role of the bonding potentials and that of the structural descriptions (beams and trusses) of the original Molecular Mechanics (MM) model. The energetic differences between structural models and MM models will be highlighted through exact discrete homogenization procedure. By the way, some theoretical expression of graphene elastic constants available in the literature are recovered and supported by numerical experimentation. The results provide also an assessment of the accuracy of the selected potentials with repost to both ab-initio reference solutions and the experimental measurements available. Some suggestions towards a reparametrization of the modified Morse potential are consequently formulated.