This article addresses the asymptotic response of viscoelastic heterogeneous media in the frequency domain, at high and low frequencies, for different types of elementary linear viscoelastic constituents. By resorting to stationary principles for complex viscoelasticity and adopting a classification of the viscoelastic behaviours based on the nature of their asymptotic regimes, either elastic or viscous, four exact relations are obtained on the overall viscoelastic complex moduli in each case. Two relations are related to the asymptotic uncoupled heterogeneous problems, while the two remaining ones result from the viscoelastic coupling that manifests itself in the transient regime. These results also provide exact conditions on certain integrals in time of the effective relaxation spectrum. This general setting encompasses the results obtained in preceding studies on mixtures of Maxwell constituents [1,2].
Dans cette Note, nous étudions la réponse asymptotique de milieux hétérogènes viscoélastiques dans le domaine fréquentiel, à basse et haute fréquence, pour les différents types de constituants viscoélastiques linéaires élémentaires. En ayant recours à des principes de stationnarité pour la viscoélasticité complexe et en utilisant une classification des comportements viscoélastiques fondée sur la nature des régimes asymptotiques, élastique ou visqueux, quatre relations exactes sont obtenues sur les modules complexes effectifs. Deux d'entre elles décrivent les régimes asymptotiques effectifs (problèmes hétérogènes découplés), tandis que deux autres résultent du couplage viscoélastique qui se manifeste au cours du régime transitoire. Ces résultats fournissent également des conditions exactes sur des intégrales temporelles du spectre de relaxation effectif. Ce cadre général inclut les résultats précédemment obtenus pour des mélanges de constituants maxwelliens [1,2].
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Mots-clés : Viscoélasticité, Matériaux composites, Homogénéisation
Valentin Gallican 1; Renald Brenner 1; Pierre Suquet 2
@article{CRMECA_2017__345_11_742_0,
author = {Valentin Gallican and Renald Brenner and Pierre Suquet},
title = {Exact asymptotic relations for the effective response of linear viscoelastic heterogeneous media},
journal = {Comptes Rendus. M\'ecanique},
pages = {742--751},
publisher = {Elsevier},
volume = {345},
number = {11},
year = {2017},
doi = {10.1016/j.crme.2017.09.001},
language = {en},
}
TY - JOUR AU - Valentin Gallican AU - Renald Brenner AU - Pierre Suquet TI - Exact asymptotic relations for the effective response of linear viscoelastic heterogeneous media JO - Comptes Rendus. Mécanique PY - 2017 SP - 742 EP - 751 VL - 345 IS - 11 PB - Elsevier DO - 10.1016/j.crme.2017.09.001 LA - en ID - CRMECA_2017__345_11_742_0 ER -
%0 Journal Article %A Valentin Gallican %A Renald Brenner %A Pierre Suquet %T Exact asymptotic relations for the effective response of linear viscoelastic heterogeneous media %J Comptes Rendus. Mécanique %D 2017 %P 742-751 %V 345 %N 11 %I Elsevier %R 10.1016/j.crme.2017.09.001 %G en %F CRMECA_2017__345_11_742_0
Valentin Gallican; Renald Brenner; Pierre Suquet. Exact asymptotic relations for the effective response of linear viscoelastic heterogeneous media. Comptes Rendus. Mécanique, Volume 345 (2017) no. 11, pp. 742-751. doi : 10.1016/j.crme.2017.09.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.09.001/
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