Comptes Rendus
On the space-time separated representation of integral linear viscoelastic models
Comptes Rendus. Mécanique, Volume 343 (2015) no. 4, pp. 247-263.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2015.02.002
Keywords: PGD, Viscoelasticity, Integro-differential models, Fatigue
Mots-clés : PGD, Viscoélasticité, Modèle integro-differentiel, Fatigue

Amine Ammar 1, 2; Ali Zghal 1; Franck Morel 2; Francisco Chinesta 3

1 UMSSDT, ENSIT, Université de Tunis, 5, avenue Taha-Hussien, Montfleury 1008, Tunis, Tunisia
2 Arts et Métiers ParisTech, 2, bd du Ronceray, BP 93525, 49035 Angers cedex 01, France
3 GEM, UMR CNRS–Centrale Nantes, 1, rue de la Noe, BP 92101, 44321 Nantes cedex 3, France
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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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