Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations

The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into the different types of plate theory namely as classical plate theory (CLPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theory (HSDT). An exact solution is conducted to obtain the critical biaxial buckling loads of simply-supported square and rectangular SLGSs with various values of side-length and nonlocal parameter corresponding to each type of nonlocal plate model. Then, molecular dynamics (MD) simulations are performed for a series of armchair and zigzag SLGSs with different side-lengths, the results of which are matched with those obtained by the nonlocal plate models to extract the appropriate values of nonlocal parameter relevant to each type of nonlocal elastic plate model and chirality. It is found that the present nonlocal plate models with their proposed proper values of nonlocal parameter have an excellent capability to predict the biaxial buckling response of SLGSs.