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Comptes Rendus. Physique
Analysis of the delayed damage model for three one-dimensional loading scenarii
Comptes Rendus. Physique, Volume 21 (2020) no. 6, pp. 527-537.

Part of the special issue: Prizes of the French Academy of Sciences 2019 (continued)

The delayed damage model has been introduced by Allix and Deü [] as a way to overcome spurious mesh dependency in failure analysis involving damage and dynamic loading. The damage rate is bounded through a time scale which, combined with the wave speed, introduces implicitly a length scale. In this paper, the delayed damage model is analyzed through numerical experiments on three different loading cases of a bar: a slow loading leading to a dynamic failure, pulses and impact. We observe and discuss the load level needed for failure (and the dependence of this load level with respect to the loading rate), as well as the dissipation and extent of the fully damaged zone at failure. Observations lead to the following conclusions. First, the delayed damage model has no regularization effect for a dynamic failure initiating from rest. Second, for pulse loadings, the loading rate has no influence on the minimal load level needed for failure (even though the delayed damage model is a time-dependent model), and beyond this minimal load level for failure, the extent of the fully damage zone rises, proportionally to the length scale. Third, regarding the impact, the velocity needed to reach failure depends only the time-independent parameters of the models, and not the ones linked to the delayed damage.

Le modèle d’endommagement à effet retard a été introduit par Allix et Deü [] pour surmonter dans le cas de chargement dynamique la dépendance de maillage non-physique observée dans l’analyse de rupture. Le taux d’endommagement est limité via un temps caractéristique qui, combiné à la vitesse des ondes, introduit implicitement une longueur caractéristique. Dans cet article, le modèle d’endommagement à effet retard est analysé par des simulations numériques sur trois cas de chargement différents d’une barre : un chargement lent conduisant à une rupture dynamique, des impulsions et un impact. Nous observons et discutons le niveau de charge nécessaire à la rupture (et la dépendance de ce niveau de charge à la vitesse du chargement), ainsi que la dissipation et l’étendue de la zone entièrement endommagée lors de la rupture. Les observations conduisent aux conclusions suivantes. Premièrement, le modèle à effet retard n’a aucun effet de régularisation pour une défaillance dynamique démarrant du repos. Deuxièmement, pour les chargements par impulsions, la vitesse de chargement n’a aucune influence sur le niveau de charge minimal nécessaire à la rupture (alors que le modèle à effet retard est pourtant un modèle dépendant du temps), et au-delà de ce niveau de charge minimal pour la rupture, l’étendue du dommage total est proportionnelle à la longueur caractéristique. Troisièmement, en ce qui concerne l’impact, la vitesse nécessaire pour atteindre la rupture dépend uniquement des paramètres affectant la version indépendante du modèle (et non ceux liés à l’effet retard).

Published online:
DOI: 10.5802/crphys.42
Keywords: Damage, Delay effect, Dynamics, Localization, Softening
Jihed Zghal 1; Nicolas Moës 2, 3

1 Laboratoire Energetique Mecanique Electromagnetisme (LEME), University of Paris Nanterre, 50 rue de sèvres 92410 Ville d’Avray, France
2 Ecole Centrale de Nantes, GeM Institute, UMR CNRS 6183, 1 rue de la Noë, 44321 Nantes, France
3 Institut Universitaire de France (IUF), France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Jihed Zghal; Nicolas Moës. Analysis of the delayed damage model for three one-dimensional loading scenarii. Comptes Rendus. Physique, Volume 21 (2020) no. 6, pp. 527-537. doi : 10.5802/crphys.42. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.42/

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