[Représentation séparée espace-temps pour des comportements viscoélastiques linaires intégraux]
L'analyse du comportement mécanique des matériaux entraîne de nombreuses difficultés du point de vue numérique. Dans ce travail, nous allons nous focaliser sur l'une d'entre elles, celle associée à la simulation transitoire du comportement mécanique quand l'intervalle temporel d'intérêt est substantiellement plus long que le temps caractéristique associé à la réponse mécanique. Cette situation est fréquemment retrouvée dans la caractérisation rhéologique des matériaux viscoélastiques (pour la détermination du module complexe) ainsi que quand on s'attaque à la simulation de la fatigue. De plus, dans le cas des matriaux viscoélastiques, le comportement est généralement décrit par une loi de comportement intégrale qui évite le besoin d'utiliser des variables internes, donnant lieu à un modèle mécanique integro-différentiel. Pour une résolution efficace, nous analysons ici l'utilisation d'une représentation séparée en espace-temps.
The analysis of materials mechanical behavior involves many computational challenges. In this work, we are addressing the transient simulation of the mechanical behavior when the time of interest is much larger than the characteristic time of the mechanical response. This situation is encountered in many applications, as for example in the simulation of materials aging, or in structural analysis when small-amplitude oscillatory loads are applied during a long period, as it occurs for example when characterizing viscoelastic behaviors by calculating the complex modulus or when addressing fatigue simulations. Moreover, in the case of viscoelastic behaviors, the constitutive equation is many times expressed in an integral form avoiding the necessity of using internal variables, fact that results in an integro-differential model. In order to efficiently simulate such a model, we explore in this work the use of a space-time separated representation.
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Mot clés : PGD, Viscoélasticité, Modèle integro-differentiel, Fatigue
@article{CRMECA_2015__343_4_247_0,
author = {Amine Ammar and Ali Zghal and Franck Morel and Francisco Chinesta},
title = {On the space-time separated representation of integral linear viscoelastic models},
journal = {Comptes Rendus. M\'ecanique},
pages = {247--263},
publisher = {Elsevier},
volume = {343},
number = {4},
year = {2015},
doi = {10.1016/j.crme.2015.02.002},
language = {en},
}
TY - JOUR AU - Amine Ammar AU - Ali Zghal AU - Franck Morel AU - Francisco Chinesta TI - On the space-time separated representation of integral linear viscoelastic models JO - Comptes Rendus. Mécanique PY - 2015 SP - 247 EP - 263 VL - 343 IS - 4 PB - Elsevier DO - 10.1016/j.crme.2015.02.002 LA - en ID - CRMECA_2015__343_4_247_0 ER -
%0 Journal Article %A Amine Ammar %A Ali Zghal %A Franck Morel %A Francisco Chinesta %T On the space-time separated representation of integral linear viscoelastic models %J Comptes Rendus. Mécanique %D 2015 %P 247-263 %V 343 %N 4 %I Elsevier %R 10.1016/j.crme.2015.02.002 %G en %F CRMECA_2015__343_4_247_0
Amine Ammar; Ali Zghal; Franck Morel; Francisco Chinesta. On the space-time separated representation of integral linear viscoelastic models. Comptes Rendus. Mécanique, Volume 343 (2015) no. 4, pp. 247-263. doi : 10.1016/j.crme.2015.02.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.02.002/
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