[Étude unidimensionnelle des effets de bords et de diffusion de l’endommagement pour des modèles d’endommagement régularisés]
Les modèles d’endommagement classiques ne sont pas capables de représenter l’ensemble du processus de dégradation ayant lieu pendant l’adoucissement en déformation. Dans le cadre de la méthode des éléments finis, des résultats dépendants du maillage sont obtenus. Des modèles non-locaux sont généralement utilisés pour régulariser la réponse structurelle et retrouver l’objectivité vis-à-vis du maillage. Cependant, certaines incohérences physiques peuvent être observées, telles que la diffusion progressive de l’endommagement et son attraction par la frontière du domaine. Les approches non-locales avec interactions évolutives peuvent mieux décrire le processus de fissuration et surmonter ces problèmes. Dans cet article, le test d’écaillage est utilisé pour souligner certains inconvénients et avantages typiques de différentes méthodes de régularisation. En particulier, l’attention est portée sur la formulation intégrale non-locale sur la variable interne du modèle de comportement, sur une formulation à gradient implicite, sur une approche intégrale non-locale basée sur les contraintes et sur l’approche non-locale dite eikonale. Dans ce dernier cas, ses formulations intégrales et de type gradient sont considérées.
Local Continuum Damage Mechanics models cannot represent the entire degradation process in materials exhibiting strain-softening behaviors. It is well known that the rate equilibrium problem becomes ill-posed when softening occurs, and an infinity of solutions exists. From a numerical point of view, finite element analyses suffer from mesh-dependent results. Non-local models are generally used to regularize the structural response and recover objectivity. However, some physical inconsistencies can be observed in numerical results, e.g., damage diffusion over large damaged bands and damage attraction on the boundary of the computational domain. Non-local formulations with evolving interactions may better describe the damaging process and overcome these issues. This paper uses the so-called spalling test to underline the main drawbacks and advantages of several regularized models with constant and evolving non-local interactions. Concerning non-local formulations with constant interactions, attention is focused on the integral non-local formulation on the internal variable of the constitutive model and an implicit gradient damage formulation. Regarding formulations with evolving non-local interactions, attention is focused on a “stress-based integral non-local” approach and the so-called “eikonal non-local” approach. In this latter case, both its integral-type and gradient-type variants are considered.
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Mot clés : Endommagement, Régularisation non-locale, Écaillage, Bords, Diffusion de l’endommagement
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@article{CRMECA_2022__350_G3_507_0,
author = {Breno Ribeiro Nogueira and C\'edric Giry and Giuseppe Rastiello and Fabrice Gatuingt},
title = {One-dimensional study of boundary effects and damage diffusion for regularized damage models},
journal = {Comptes Rendus. M\'ecanique},
pages = {507--546},
publisher = {Acad\'emie des sciences, Paris},
volume = {350},
year = {2022},
doi = {10.5802/crmeca.137},
language = {en},
}
TY - JOUR AU - Breno Ribeiro Nogueira AU - Cédric Giry AU - Giuseppe Rastiello AU - Fabrice Gatuingt TI - One-dimensional study of boundary effects and damage diffusion for regularized damage models JO - Comptes Rendus. Mécanique PY - 2022 SP - 507 EP - 546 VL - 350 PB - Académie des sciences, Paris DO - 10.5802/crmeca.137 LA - en ID - CRMECA_2022__350_G3_507_0 ER -
%0 Journal Article %A Breno Ribeiro Nogueira %A Cédric Giry %A Giuseppe Rastiello %A Fabrice Gatuingt %T One-dimensional study of boundary effects and damage diffusion for regularized damage models %J Comptes Rendus. Mécanique %D 2022 %P 507-546 %V 350 %I Académie des sciences, Paris %R 10.5802/crmeca.137 %G en %F CRMECA_2022__350_G3_507_0
Breno Ribeiro Nogueira; Cédric Giry; Giuseppe Rastiello; Fabrice Gatuingt. One-dimensional study of boundary effects and damage diffusion for regularized damage models. Comptes Rendus. Mécanique, Volume 350 (2022), pp. 507-546. doi : 10.5802/crmeca.137. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.137/
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