Small scale effect on the buckling of single-layered graphene sheets under biaxial compression via nonlocal continuum mechanics

In this article, the small scale effect on the buckling analysis of biaxially compressed single-layered graphene sheets (SLGS) is studied using nonlocal continuum mechanics. The nonlocal mechanics accounts for the small size effects when dealing with nano size elements such as graphene sheets. Using the principle of virtual work the governing equations are derived for rectangular nanoplates. Solutions for buckling loads are computed using differential quadrature method (DQM). It is shown that the nonlocal effect is quite significant in graphene sheets and has a decreasing effect on the buckling loads. When compared with uniaxially compressed graphene, the biaxially compressed one show lower influence of nonlocal effects for the case of smaller side lengths and larger nonlocal parameter values. This difference in behavior between uniaxial and biaxial compressions decreases as the size of the graphene sheets increases.