Microstructure-informed reduced modes synthesized with Wang tiles and the Generalized Finite Element Method

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F21%3A00351354" target="_blank" >RIV/68407700:21110/21:00351354 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/s00466-021-02028-y" target="_blank" >https://doi.org/10.1007/s00466-021-02028-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00466-021-02028-y" target="_blank" >10.1007/s00466-021-02028-y</a>

Result language

angličtina

Original language name

Microstructure-informed reduced modes synthesized with Wang tiles and the Generalized Finite Element Method

Original language description

A recently introduced representation by a set of Wang tiles-a generalization of the traditional Periodic Unit Cell-based approach-serves as a reduced geometrical model for materials with stochastic heterogeneous microstructure, enabling an efficient synthesis of microstructural realizations. To facilitate macroscopic analyses with a fully resolved microstructure generated with Wang tiles, we develop a reduced order modelling scheme utilizing pre-computed characteristic features of the tiles. In the offline phase, inspired by computational homogenization, we extract continuous fluctuation fields from the compressed microstructural representation as responses to generalized loading represented by the first- and second-order macroscopic gradients. In the online phase, using the ansatz of the generalized finite element method, we combine these fields with a coarse finite element discretization to create microstructure-informed reduced modes specific for a given macroscopic problem. Considering a two-dimensional scalar elliptic problem, we demonstrate that our scheme delivers less than 3% error in both the relative L-2 and energy norms with only 0.01% of the unknowns when compared to the fully resolved problem. Accuracy can be further improved by locally refining the macroscopic discretization and/or employing more pre-computed fluctuation fields. Finally, unlike standard snapshot-based reduced-order approaches, our scheme handles significant changes in the macroscopic geometry or loading without the need for recalculating the offline phase, because the fluctuation fields are extracted without any prior knowledge of the macroscopic problem.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

20302 - Applied mechanics

Project

<a href="/en/project/GX19-26143X" target="_blank" >GX19-26143X: Non-periodic pattern-forming metamaterials: Modular design and fabrication</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Computational Mechanics

ISSN

0178-7675

e-ISSN

1432-0924

Volume of the periodical

68

Issue of the periodical within the volume

2

Country of publishing house

DE - GERMANY

Number of pages

21

Pages from-to

233-253

UT code for WoS article

000653613000001

EID of the result in the Scopus database

2-s2.0-85106441436