Open Access

ARTICLE

A New Molecular Structural Mechanics Model for the Flexural Analysis of Monolayer Graphene

G. Shi ¹, P. Zhao ¹

1 Department of Mechanics, Tianjin University, Tianjin 30072, China.

Computer Modeling in Engineering & Sciences 2011, 71(1), 67-92. https://doi.org/10.3970/cmes.2011.071.067

Abstract

Based on molecular mechanics and the concept of flexible connection used in the flexibly connected frames, a new structural mechanics model, a 2-D frame composed of anisotropic beams and flexible connections, is proposed for the simulation of the static and dynamic flexural behavior of monolayer graphene. The equivalent beam representing the C-C bond in the new molecular structural mechanics (MSM) model has two salient features compared with other MSM models presented for the analysis of carbon nanotubes: one is that the flexible connections at the beam ends are used to account for the bond-angle variations between the C-C bonds of graphene; and the other is that there are two principal flexural rigidities used for the flexible connections to reflect the different behaviors of the s-bond and p-bond in the graphene lattice. The mechanical properties of the equivalent beam for the C-C bond of graphene lattice are evaluated from the force constants of graphene given by molecular mechanics. The in-plane Young's moduli, Poisson ratios, equivalent flexural rigidities and the flexural frequencies of monolayer graphene are simulated using the proposed new MSM model coupled with ANSYS. The simulation results show that the 2-D flexibly connected frame of the new MSM model proposed in this paper gives improved predictions of the in-plane Young's moduli, Poisson ratios and flexural rigidities of monolayer graphene than other MSM models. The present study also indicates that monolayer graphene is kind of an orthotropic material since both the in-plane elastic constants and the flexural rigidities of monolayer graphene are the principal directions dependent.

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