An analytical approach to determination of bending modulus of a multi-layered graphene sheet

In this paper, the bending modulus of a multi-layered graphene sheet is investigated using a geometrically based analytical approach. For this purpose, a bending potential energy is derived, based on the van der Waals interactions of atoms belonging to the two neighboring sheets of a double-layered graphene sheet. The inter-atomic spacing between the adjacent layers is determined along the line of action of the applied bending moments. The bending potential of the double-layered sheet is calculated by summing up the potentials at discrete hexagons over the length and width of the sheet. A multi-layered graphene sheet is considered as consisting of many stacking double-layers. It is observed that the bending modulus of a multi-layered graphene sheet does not depend on the length of the sheet and is a property for the multi-layered sheet.