Application of Nonlocal Elasticity Theory to Modelling of Two-Dimensional Structures

The mechanical properties of a graphene layer are fixed by the strength and stability of its carbon bonds. In a graphene sheet, every carbon atom is available for bonding with three other nearest neighbour atoms, forming strong planar \(\sigma \)-bonds with them. In graphite, however, this layer is rather very weakly bonded to other layers via vertical \(\pi \)-bonds [1]. The exotic mechanical properties of graphene play a significant role in various applications, and they also affect the other properties of graphene; for instance, its mechanical deformation promotes changes in its electronic structure [2]. The exotic mechanical properties of graphene play a significant role in various applications, and they also affect the other properties of graphene; for instance, its mechanical deformation promotes changes in its electronic structure [2]. Thus, the mechanical properties of graphene must be carefully studied to enhance its application potential. Even though the discovery of the graphene sheet has a very short history, it is very significant that its mechanical properties have been studied in an unusually significant number of papers employing the nonlocal continuum theory. In this chapter, the mechanical behaviour of the graphene sheets will be discussed via the nonlocal plate models. Simple analytical relations are derived to determine their bending behaviour, the natural frequencies and the buckling loads.