The buckling of graphene sheets on substrates can significantly degrade their performance in materials and devices. Therefore, a systematic investigation on the buckling behavior of monolayer graphene sheet/substrate systems is carried out in this paper by both molecular mechanics simulations and theoretical analysis. From 70 simulation cases of simple-supported graphene sheets with different sizes under uniaxial compression, two different buckling modes are investigated and revealed to be dominated by the graphene size. Especially, for graphene sheets with length larger than 3 nm and width larger than 1.1 nm, the buckling mode depends only on the length/width ratio. Besides, it is revealed that the existence of graphene substrate can increase the critical buckling stress and strain to 4.39 N/m and 1.58%, respectively, which are about 10 times those for free-standing graphene sheets. Moreover, for graphene sheets with common size (longer than 20 nm), both theoretical and simulation results show that the critical buckling stress and strain are dominated only by the adhesive interactions with substrate and independent of the graphene size. Results in this work provide valuable insight and guidelines for the design and application of graphene-derived materials and nano-electromechanical systems.

Interlayer shear between graphene sheets plays an important role in graphene-based materials and devices, but the effect of in-plane deformation of graphene, which may depend on the graphene size, has not been fully understood. In this paper, the size effect on interlayer shear behavior between two graphene sheets is studied based on a non-linear shear-lag model with energy barrier analysis, in which both the lattice registry effect and the elastic deformation of graphene are taken into account, and molecular dynamics (MD) simulations are carried out to verify the model. Both theoretical prediction and MD simulations show that the maximum interlayer shear force of short graphene sheets increases with the graphene length and width. However, if the sheet length is beyond 20 nm, the maximum shear force cannot be further increased by increasing the graphene length due to the non-uniform relative displacement between graphene layers, which is caused by the in-plane deformation of graphene. The upper bound of the maximum shear force per unit graphene width is obtained analytically as a constant 5.6 N/m, suggesting that a small force can pull an infinite long graphene belt to slide on a graphene substrate. This study offers useful information for design and manufacture of graphene-based nano-devices and materials.