Equivalent Young's modulus and thickness of graphene sheets for the continuum mechanical models

Abstract

The Young's modulus and the thickness of graphene sheets (GSs) are the two major material constants when continuum mechanical models are used to analyze the mechanical behaviors of GSs. It should be pointed out that the equivalent Young's modulus and the thickness of GSs should correspond to both stretching and bending loading conditions. In this Letter, the same as “Yakobson paradox,” we predicted the equivalent Young's modulus and the thickness of GSs using an analytical method linked with an atomic interaction based continuum model and a continuum elastic model. Based on the proposed method, by unifying the Young's modulus of GSs in the cases of both stretching and bending, and by determining the matching thickness in the same time, the equivalent Young's modulus and the thickness of GSs utilized in continuum mechanical models are calculated and proposed to be 2.81 TPa and 1.27 Å, respectively.