A method for developing the equivalent continuum model of a single layer graphene sheet

A method is presented to develop the equivalent continuum model for a single-layered graphene sheet. This method integrates molecular dynamics method as an exact numerical solution with theory of shell as an analytical method. The force-depth results achieved from molecular dynamics simulation of nano-indentation of a single graphene sheet are compared with the formulation for large deflection of circular plates loaded at the centre. As a result, the effective Young's modulus and mechanical thickness of the sheet wall are independently obtained. The validity of this approach is verified by comparing finite element modeling of nano-indentation of a single graphene sheet with molecular dynamics results available in the literature. Presented results demonstrate that the proposed method could provide a valuable tool for studying the mechanical behaviour of single-layered graphene sheets, as well as efficiency of continuum theory in nano-structured material.