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Data-driven Reduced Homogenization for Transient Diffusion Problems with Emergent History Effects

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.
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Contributor : Thomas Heuzé <>
Submitted on : Monday, April 5, 2021 - 1:42:53 PM
Last modification on : Wednesday, April 7, 2021 - 3:22:44 AM

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Abdullah Waseem, Thomas Heuzé, Marc G.D. Geers, Varvara Kouznetsova, Laurent Stainier. Data-driven Reduced Homogenization for Transient Diffusion Problems with Emergent History Effects. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2021, 380, pp.113773. ⟨10.1016/j.cma.2021.113773⟩. ⟨hal-03189901⟩

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