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Estimating the elastic properties of few-layer graphene from the free-standing indentation response

Using molecular mechanics simulations, the elastic properties of multi-layer graphene (MLG) are investigated; this includes both the linear analysis based on the indentation load–displacement relationship and the nonlinear analysis based on the strain energy. The elastic properties of graphene layers in MLG are similar to each other and also quite close to those of monolayer graphene. The van der Waals (VDW) interaction between graphene layers (interlayer interaction) will create a difference between the indenter tip displacement and the deviation of MLG in indentation, which will cause an overestimation of the elastic modulus of MLG based on classic indentation analysis. This overestimation can be as high as 20%. In addition, the interlayer interaction will significantly affect the nonlinear elastic behavior of MLG in free-standing indentation. With an increase in the number of layers of MLG, the second-order elastic stiffness of MLG is very sensitive to the indentation loading range, and the third-order nonlinear elastic constant is significantly increased.