Homogenization approach and Floquet-Bloch theory for wave analysis in fluid-saturated porous media with mesoscopic heterogeneities

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F21%3A43959412" target="_blank" >RIV/49777513:23520/21:43959412 - isvavai.cz</a>

Výsledek na webu

<a href="http://hdl.handle.net/11025/42920" target="_blank" >http://hdl.handle.net/11025/42920</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apm.2020.08.044" target="_blank" >10.1016/j.apm.2020.08.044</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Homogenization approach and Floquet-Bloch theory for wave analysis in fluid-saturated porous media with mesoscopic heterogeneities

Popis výsledku v původním jazyce

We consider fluid-saturated poroelastic media whose the mechanical response is governed by the Biot model relevant to a mesoscopic scale. Assuming the material properties being described by periodic functions, to analyze wave propagation in such heterogeneous and anisotropic media, we derive a formulation based on the Floquet-Bloch (FB) wave decomposition which enables to analyze waves within the whole first Brillouin zone associated with the periodic structure. The wave dispersion results obtained by the FB approach are compared with those computed using a model derived by the homogenization based on the asymptotic analysis with respect to the scale parameter. As another new ingredient, the homogenized model is extended to describe media saturated simultaneously by multiple different fluids, so that the model involves new permeability tensors and differs in structure from the model derived earlier. The dispersion analysis by the FB approach leads to a cumbersome quadratic eigenvalue problem to be solved for complex wave numbers. We suggest an efficient filtration strategy to identify the principle propagating modes (the fast and slow compressional waves and the shear waves). For comparison with results of the FB transformation applied at the mesoscopic heterogeneity scale, the homogenized model responses are reconstructed using the corrector results of the homogenization with fixing a finite scale. Numerical examples illustrate very good correspondence of the dispersion results, as computed by both the approaches.

Název v anglickém jazyce

Homogenization approach and Floquet-Bloch theory for wave analysis in fluid-saturated porous media with mesoscopic heterogeneities

Popis výsledku anglicky

We consider fluid-saturated poroelastic media whose the mechanical response is governed by the Biot model relevant to a mesoscopic scale. Assuming the material properties being described by periodic functions, to analyze wave propagation in such heterogeneous and anisotropic media, we derive a formulation based on the Floquet-Bloch (FB) wave decomposition which enables to analyze waves within the whole first Brillouin zone associated with the periodic structure. The wave dispersion results obtained by the FB approach are compared with those computed using a model derived by the homogenization based on the asymptotic analysis with respect to the scale parameter. As another new ingredient, the homogenized model is extended to describe media saturated simultaneously by multiple different fluids, so that the model involves new permeability tensors and differs in structure from the model derived earlier. The dispersion analysis by the FB approach leads to a cumbersome quadratic eigenvalue problem to be solved for complex wave numbers. We suggest an efficient filtration strategy to identify the principle propagating modes (the fast and slow compressional waves and the shear waves). For comparison with results of the FB transformation applied at the mesoscopic heterogeneity scale, the homogenized model responses are reconstructed using the corrector results of the homogenization with fixing a finite scale. Numerical examples illustrate very good correspondence of the dispersion results, as computed by both the approaches.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

20302 - Applied mechanics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

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

APPLIED MATHEMATICAL MODELLING

ISSN

0307-904X

e-ISSN

—

Svazek periodika

91

Číslo periodika v rámci svazku

MAR 2021

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

23

Strana od-do

1-23

Kód UT WoS článku

000606310600001

EID výsledku v databázi Scopus

2-s2.0-85092219509