Stability of a single-layer graphene sheet with various edge conditions: a non-local plate model including interatomic potentials

Abstract

In this article, the biaxial buckling of a single layer graphene sheet is investigated. The model is established through the incorporation of an interatomic potential into non-local elastic plate theory to take into account the size effects and to circumvent the use of the Young’s modulus of a single layer graphene sheet since there is no accurate value of this property available in the literature. The model links the strain energy density induced in the continuum to Eringen’s non-local constitutive relations. By using the Galerkin method, explicit formulas for the critical buckling stresses of a single layer graphene sheet with arbitrary edge supports are derived from its static deflection due to a uniformly distributed load. The influences of the small size of the system and boundary conditions on the critical buckling load of the single layer graphene sheet are studied. It is found that the critical buckling load at large side lengths is almost independent of the type of boundary condition and compressive loading and is nearly immune to size effects. The analytical expressions provide a simple and quick way to evaluate accurate values of the critical buckling load. Indeed, the lack of complexity in the formulas allows a simple prediction of the value of the scale parameter that closely matches the one obtained using the complex molecular dynamics simulation technique.