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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20302 - Applied mechanics

Projekt

<a href="/cs/project/GX19-26143X" target="_blank" >GX19-26143X: Neperiodické materiály vykazující strukturované deformace: Modulární návrh a výroba</a><br>

Návaznosti

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

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Computational Mechanics

ISSN

0178-7675

e-ISSN

1432-0924

Svazek periodika

68

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

21

Strana od-do

233-253

Kód UT WoS článku

000653613000001

EID výsledku v databázi Scopus

2-s2.0-85106441436