van der Waals effect on the nanoindentation response of free standing monolayer graphene

Using molecular mechanics simulations we investigate the elastic properties of monolayer graphene determined from free standing indentation and the effects of graphene size and indenter tip size are considered. In free standing indentation, the overall system potential energy includes two parts: the strain energy of graphene monolayer and the van der Waals (VDW) interaction energy between indenter tip and graphene. The VDW interaction will strongly affect the elastic properties of graphene monolayer determined from free standing indentation. Without considering the VDW interaction, the classical free standing indentation analysis is not able to accurately estimate the second-order elastic stiffness (E) and the third-order nonlinear elastic constant (cm) (E will be underestimated and cm will be overestimated). It is found that both E and cm determined from free standing indentation are quite close to their counterparts determined from in-plane tension after properly considering the VDW interaction. The results can provide a useful guideline to understand the elastic properties of graphene monolayer determined from free standing indentation tests.