Explicit analytical expressions for the critical buckling stresses in a monolayer graphene sheet based on nonlocal elasticity

Explicit expressions are given to study the biaxial buckling of monolayer graphene sheets. Based upon the continuum mechanics, a plate model is adopted in which the small length scale effect is incorporated into the governing equation through the nonlocal elasticity theory of Eringen. By employing the Galerkin method, analytical expressions are derived which allow quick and accurate calculation of the critical buckling loads of monolayer graphene sheets with various boundary conditions from the static deflection under a uniformly distributed load. The effectiveness of the present study is assessed by molecular dynamics simulations as a benchmark of good accuracy.

► Biaxial buckling behavior of graphene was studied based on a nonlocal plate model. ► MD simulations are performed to verify and calibrate the developed nonlocal model. ► Explicit analytical expressions for the critical buckling load of GSs were obtained for various boundary conditions. ► Explicit expressions obtained give way to quickly calibrate the scale parameter using MD results.