The non linear mechanical behaviour of single layer graphene sheets from atomistic simulation to continuum models

Single-layer graphene sheets (SLGSs) are the basic structural element of several carbon allotropes, including graphite, fullerenes and carbon nano-tubes (CNTs). Due to their remarkable mechanical properties, extensive interests have been recently devoted to characterize their behaviour at nanoscale in order to investigate also the performance of advanced composites based on their inclusions. However, the evaluation of SLGSs mechanical properties in a direct experimental way is considered a difficult task because of the technical difficulties and the costs involved in the manipulation of nanoscale objects. For these reasons several modelling tools have been proposed varying from continuum models to atomistic approaches that account for the discrete nature of the matter. The most of the existing literature has focused only the evaluation of the elastic constants and of the force constants of the interatomic potentials, instead much less studies have been made about the nonlinear SLGS behavior.