Bending Stiffness of a Double-Layered Graphene Sheet Using a Geometrically-Based Analytical Approach

In this article, the bending stiffness of a double-layered graphene sheet is investigated using a geometrically-based analytical approach. The analysis is based on the van der Waals interactions of atoms belonging to two neighboring sheets. The inter-atomic spacing between the adjacent layers is geometrically determined when the sheet is applied by a couple of moments in the opposite sides. The bending potential energy is obtained by summing up the potentials at discrete hexagons over the length and width of the sheet. It is observed that the bending stiffness of a double-layered graphene sheet does not depend on the length of the sheet and be a material property for the associated sheet.