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In this research, nano-scale continuum modeling is employed to predict Young's modulus of graphene sheet. The lattice nano-structure of a graphene sheet is replaced with a discrete space-frame structure simulating carbon-carbon bonds with either beam or spring elements. A comparative study is carried out to check the influence of employed elements on estimated Young's moduli of graphene sheets in both horizontal and vertical directions. A detailed analysis is also conducted to investigate the influence of graphene sheet sizes on its Young's modulus and corresponding aspect ratios that unwelcomed end effects disappear on the results are extracted. At the final stage, defected graphene sheets suffering from vacancy defects are investigated through a stochastic analysis taking into account both number of defects and their locations as random parameters. The reduction level in the Young's moduli of defected graphene sheets compared with non-defected ones is analyzed and reported. [ABSTRACT FROM AUTHOR]

A novel combination of concurrent and hierarchical multi-scale modeling approach is developed to predict Young's modulus of graphene/polymer composites. In this novel approach, laminate analogy and generalized method of cells are integrated into the same framework. The former takes into account orientation, while the latter is utilized to address the effect of graphene dispersions on the results. A phenomenological technique is employed for capturing various graphene dispersion inside the matrix avoiding heavy stochastic modeling. Although stochastic modeling is preferred, due to the randomness of agglomeration and orientation of embedded graphene nanosheets in the matrix, deterministic modeling is developed in this research to prevent huge computational efforts. The results are compared with previously developed stochastic modeling and more precision is observed. The developed modeling strategy is validated using published experimental observations taken from the literature by highlighting the accuracy of the proposed technique. [ABSTRACT FROM AUTHOR]

A stochastic multi-scale approach is developed for predicting elastic properties of graphene/polymer nanocomposites. All scales of nano, micro, meso and macro are travelled through a bottom-up approach using appropriate method at each scale. For each scale, separate representative volume element (RVE) is defined capturing effective parameters of that scale. Categorized under the hierarchical multi-scale modeling, the outputs of each scale are fed into the next upper scale as input data. Semi-continuum modeling is performed at the nano and micro scales, while micromechanical model is adapted for the upper scales of meso and macro. The developed modeling is implemented stochastically to address the randomness in graphene size, volume fraction, orientation, wrinkle and also formation of agglomerated particles. Therefore, stochastic multi-scale modeling is conducted accounting for process-induced uncertainties. Results show a very good agreement with experimental data available on open literature. The novelty of this research is twofold: (1) Developing of a full-range multi-scale modeling for graphene reinforced polymers starting from nano-scale and lasting to the uppermost scale of macro, (2) Full stochastic implementation of developed modeling accounting for non-deterministic parameters induced during processing graphene reinforced polymer. [ABSTRACT FROM AUTHOR]