A Nano-Micro–Macro Multiscale Modeling for Carbon Fiber-Reinforced Graphene/Epoxy Nanocomposites


A new nano-micro–macro multiscale modeling approach that combines molecular dynamic (MD) simulations with micromechanics and stochastic continuum models is proposed to model carbon-fiber-reinforced graphene/epoxy nanocomposites. Halpin–Tsai and shear lag micromechanics models are employed to relate elastic properties from MD simulations with graphene morphology (i.e., aspect ratio) and volume fraction. Uncertainties of these parameters are implemented by the Karhunen-Loève expansion (KLE) method, followed by an FE-based homogenization on a representative volume element (RVE) of carbon fiber-reinforced graphene/epoxy nanocomposite system. Elastic properties are homogenized by averaging the ensemble of RVEs with random properties. This multiscale modeling approach can be applied to the integrated computational materials engineering (ICME) for graphene-based nanocomposite materials.

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  1. 1.



l :

Graphene length

t :

Thickness of graphene layers

\(\xi\) :

l/t Aspect ratio of graphene

L i :

Correlation length in i direction

λ i :

iTh eigenvalue of the covariance kernel C

\(p_{i}\) :

iTh eigenfunction of the covariance kernel C

\({\upzeta }\) :

Normal variable

\(\phi_{i}\) :

Volume fraction of phase i

\(\theta_{GNP}\) :

Orientation angle of GNP

\(\varphi_{GNP}\) :

Orientation angle of GNP

\(C_{ijkl}\) :

Deterministic linear elastic constitutive tensor component

\(C_{ijkl}^{{\text{H}}} ( {{\text{x}},\omega } )\) :

Stochastic homogenized linear elastic constitutive tensor component

\(\Omega\) :

Coarse-scale domain

\(\Theta\) :

Fine-scale domain

\(\chi_{p}^{{{\text{kl}}}}\) :

Displacement influence function under coarse-scale strain εkl

\({\text{u}}^{\varepsilon } ( {{\text{x}},{\text{y}}} )\) :

Asymptotically expanded displacement


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This work was supported by Creative-Pioneering Researchers Program through Seoul National University (SNU) and National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (2020R1A2B5B01001899) and the Institute of Engineering Research at Seoul National University. The authors are grateful for their support.

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Correspondence to Gun Jin Yun.

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Choi, Hi., Park, C., Lim, H.J. et al. A Nano-Micro–Macro Multiscale Modeling for Carbon Fiber-Reinforced Graphene/Epoxy Nanocomposites. Multiscale Sci. Eng. (2021). https://doi.org/10.1007/s42493-021-00058-5

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  • Multiscale modeling
  • MD simulation
  • Karhunen-Loève expansion (KLE)
  • Integrated computational materials engineering (ICME)