▎ 摘　　要

Several nanomechanics formulations based on common two and three-body bonding potentials are compared. Numerical simulations and analytical approaches are used to investigate the not negligible differences among the predictions of the in-plane elastic constants of graphene sheets in the literature, separately exploring the role of the potentials and that of the structural descriptions (beams and trusses) of the original molecular mechanics (MM) model. The energetic differences between the structural models and the MM model are highlighted through exact discrete homogenization procedures. In so doing, some theoretical expressions of the graphene elastic constants available in the literature are recovered and supported by the numerical experimentation. The results provide also an assessment of the accuracy of some potentials largely employed in the literature with respect to several ab-initio reference solutions and the experimental measurements available. Some suggestions towards a reparametrization of the modified Morse potential are consequently formulated. (C) 2016 Elsevier Ltd. All rights reserved.