Continuum Plate Theory and Atomistic Modeling to Find the Flexural Rigidity of a Graphene Sheet Interacting with a Substrate

Table 1

List of variables and constants.

Symbol	Description	Units
𝑢	Deflection of the free graphene sheet	nm
𝑙	Length of the free graphene sheet in the 𝑥 direction	nm
𝑤	Width of the free graphene sheet in the 𝑦 direction	nm
𝑑	Initial separation between the two graphene sheets	nm
𝑇	Lateral force on the free graphene sheet	nN/nm
𝑓(𝑢+𝑑)	Transverse force on the free graphene sheet	nN/nm^2
𝛼	Flexural Rigidity of a graphene sheet	nN nm
𝑐12, 𝑐6	Constants for the Lennard-Jones (12-6) potential	nN nm^13, nN nm^7
𝜎	Density of a graphene sheet	atoms/nm^2