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The main purpose of the present research is analytical and numerical analyses of graphene/epoxy nanocomposites with a random distribution of nanoparticles. For this purpose, by combining the molecular dynamics and micromechanics methods, a new approach is presented. The molecular dynamics method is used to model the stiffness of the graphene/epoxy nanocomposites containing one layer of nano graphene embedded in epoxy resin. A multi-scale modeling strategy from macro to meso, then from meso to micro and finally from micro to nano scales is introduced. A representative volume element (RVE) is selected and for a nanocomposite having a single monolayer graphene embedded in epoxy resin, the longitudinal (E11), transverse (E22) and normal (E33) stiffnesses for three RVEs with arbitary graphene size are simulated. The best curve is fitted to each stiffness diagram and stiffnesses of the RVE in three directions with true graphene size are investigated. In order to consider the effect of randomly graphene sheets distribution in epoxy resin, micromechanical approach is used. Finally, the stiffness of the nanocomposites with randomly distributed graphene is calculated. For evaluation of the present approach in this research an experimental program is conducted. The result of the modeling is well agreed with the experimental data.

Keywords: Stiffness, Graphene, nanocomposites, Molecular Dynamics, Micromechanics

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