A data-driven computational homogenization method based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites

  • Xiaoxin Lu
  • Dimitris G. Giovanis
  • Julien YvonnetEmail author
  • Vissarion Papadopoulos
  • Fabrice Detrez
  • Jinbo Bai
Original Paper


In this paper, a data-driven-based computational homogenization method based on neural networks is proposed to describe the nonlinear electric conduction in random graphene-polymer nanocomposites. In the proposed technique, the nonlinear effective electric constitutive law is provided by a neural network surrogate model constructed through a learning phase on a set of RVE nonlinear computations. In contrast to multilevel (FE\(^2\)) methods where each integration point is associated with a full nonlinear RVE calculation, the nonlinear macroscopic electric field-electric flux relationship is efficiently evaluated by the surrogate neural network model, reducing drastically (by several order of magnitudes) the computational times in multilevel calculations. Several examples are presented, where the RVE contains aligned graphene sheets embedded in a polymer matrix. The nonlinear behavior is due to the modeling of the tunelling effect at the scale of graphene sheets.


Multiscale analysis Data-driven analysis Graphene nanocomposites Homogenization Electric behavior Artificial neural network 



The financial support from Institut Universitaire de France (IUF) is gratefully acknowledged for JY.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Xiaoxin Lu
    • 1
  • Dimitris G. Giovanis
    • 2
  • Julien Yvonnet
    • 1
    Email author
  • Vissarion Papadopoulos
    • 3
  • Fabrice Detrez
    • 1
  • Jinbo Bai
    • 4
  1. 1.Laboratoire Modélisation et Simulation Multi Échelle, MSME UMR 8208 CNRSUniversité Paris-EstMarne-la-ValléeFrance
  2. 2.Department of Civil EngineeringJohns Hopkins UniversityBaltimoreUSA
  3. 3.Department of Civil EngineeringNational Technical University of AthensAthensGreece
  4. 4.Laboratoire de Mécanique des Sols, Structures et Matériaux, UMR 8579 CNRSUniversité Paris SaclayParisFrance

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