An atomistic-continuum multiscale approach to determine the exact thickness and bending rigidity of monolayer graphene

Abstract

In this paper, we employ the atomistic-continuum method to open a new way to precisely measure the thickness of one-atomic material. The wall thickness of graphene is exactly extracted to be 0.0739 nm by fitting the first eight natural frequencies of a series of simply-supported graphene using atomistic-continuum method with classical plate theory. The Young's modulus and bending rigidity are determined to be 3.1851 TPa and 0.8066 eV. By using this thickness, the free vibration studies of clamped case, which removes the effect of dangling bonds, by the atomistic-continuum method, molecular mechanics and classical plate theory are found to be in a good agreement, confirming its accuracy. Inherited it to the hollow tubular structure, it is found that both Timoshenko and Euler-Bernoulli beam models also give a quite close prediction of carbon nanotubes as compared with molecular mechanics. This means the discrepancy between atomic simulation and continuum mechanics is no other than the unreal wall thickness. Besides, the usage of scale parameter and its value is also discussed.