Buckling analysis of multi-layered graphene sheets based on a continuum mechanics model

In this paper, buckling analysis of biaxially compressed multi-layered graphene sheets with a continuum plate model is reported. The equations of motion are analytically solved to obtain closed-form solution for buckling loads of all edges simply supported multi-layered graphene sheets. The interaction of van der Waals (vdWs) pressure between the layers is incorporated in the formulation to determine the buckling behavior of simply supported MLGSs. Explicit formulae are derived for predicting the critical buckling loads of double- and triple-layered graphene sheets, and they clearly indicate the effect of vdW interaction on the critical buckling loads. The critical buckling loads are calculated for various numbers of layered graphene sheets, and the obtained results show that the vdW force has no effect on the first critical buckling load of an MLGS, but plays a significant role in all higher first critical buckling loads for all combinations of m and n.