Data-driven reduced homogenization for transient diffusion problems with emergent history effects

Abdullah Waseem, Thomas Heuzé, Marc G.D. Geers, Varvara G. Kouznetsova, Laurent Stainier (Corresponding author)

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Abstract

In this paper, we propose a data-driven reduced homogenization technique to capture diffusional phenomena in heterogeneous materials which reveal, on a macroscopic level, a history-dependent non-Fickian behavior. The adopted enriched-continuum formulation, in which the macroscopic history-dependent transient effects are due to the underlying heterogeneous microstructure is represented by enrichment-variables that are obtained by a model reduction at the micro-scale. The data-driven reduced homogenization minimizes the distance between points lying in a data-set and points associated with the macroscopic state of the material. The enrichment-variables are excellent pointers for the selection of the correct part of the data-set for problems with a time-dependent material state. Proof-of-principle simulations are carried out with a heterogeneous linear material exhibiting a relaxed separation of scales. Information obtained from simulations carried out at the micro-scale on a unit-cell is used to determine approximate values of metric coefficients in the distance function. The proposed data-driven reduced homogenization also performs adequately in the case of noisy data-sets. Finally, the possible extensions to non-linear history-dependent behavior are discussed.

Original languageEnglish
Article number113773
Number of pages27
JournalComputer Methods in Applied Mechanics and Engineering
Volume380
DOIs
Publication statusPublished - 1 Jul 2021

Bibliographical note

Funding Information:
Support for this research was provided by the European Commission through an Erasmus Mundus grant in the framework of the Simulation in Engineering and Entrepreneurship Development (SEED) program. The SEED program is an initiative of 8 universities Partners , managed by EACEA and financed by the European Commission with grant Ref. [2013-0043].

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

  • Computational homogenization
  • Data-driven mechanics
  • Model order reduction
  • Non-Fickian diffusion

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