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. Proofof-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.

Optimizing artificial neural networks for mechanical problems by physics‐based Rao‐Blackwellization: Example of a hyperelastic microsphere model

“…Information about the physical system can then help to reduce the required data set [3]. The idea of exploiting physical information to reduce the complexity of the problem at hand also relates to ideas from model order reduction, e.g., by training of scale separation [4] or reduced homogenization, e.g., for transient diffusion problems [5]. A hybrid multi-scale approach is used for yield-functions and evolution equations in [6].…”