Lipschitz regularization for softening material models: the Lip-field approach

Nicolas Moës; Nicolas Chevaugeon

doi:10.5802/crmeca.91

Note

Lipschitz regularization for softening material models: the Lip-field approach
[Régularisation de Lipschitz pour les modèles de matériaux adoucissants : l’approche Lip-field]

Nicolas Moës ^1,² ; Nicolas Chevaugeon ³

¹ Ecole Centrale de Nantes, GeM Institute, UMR CNRS 6183, 1 rue de la Noë, 44321 Nantes, France
² Institut Universitaire de France (IUF), France
³ Ecole Centrale de Nantes, GeM Institute, UMR CNRS 6183, 1 rue de la Noë, 44321 Nantes, France

Comptes Rendus. Mécanique, Volume 349 (2021) no. 2, pp. 415-434.

Résumé
Abstract

Les modèles de matériaux adoucissants sont connus pour déclencher des localisations parasites. Cela peut être démontré théoriquement par l’existence de solutions avec une dissipation nulle lors de la localisation et numériquement avec une dépendance de maillage et une localisation dans une seule couche d’éléments. Nous introduisons dans cet article une nouvelle façon d’éviter les localisations parasites. L’idée est d’imposer une régularité de Lipschitz sur les variables internes responsables de l’adoucissement. La contrainte de régularité introduit l’échelle de longueur nécessaire dans la formulation du matériau. De plus, nous prouvons des bornes sur le domaine affecté par cette contrainte. Une première mise en œuvre par éléments finis unidimensionnels est proposée pour l’adoucissement élastique ou plastique.

Softening material models are known to trigger spurious localizations. This may be shown theoretically by the existence of solutions with zero dissipation when localization occurs and numerically with spurious mesh dependency and localization in a single layer of elements. We introduce in this paper a new way to avoid spurious localization. The idea is to enforce a Lipschitz regularity on the internal variables responsible for the material softening. The regularity constraint introduces the needed length scale in the material formulation. Moreover, we prove bounds on the domain affected by this constraint. A first one-dimensional finite element implementation is proposed for softening elasticity and softening plasticity.

Reçu le : 2021-03-30
Révisé le : 2021-05-14
Accepté le : 2021-07-19
Publié le : 2021-08-09

DOI : 10.5802/crmeca.91

Keywords: Softening, Localization, Damage, Plasticity, Lipschitz, Lip-field
Mots-clés : Adoucissement, Localisation, Endommagement, Plasticité, Lipschitz, Lip-field

Affiliations des auteurs :

Nicolas Moës ^{1, 2} ; Nicolas Chevaugeon ³

¹ Ecole Centrale de Nantes, GeM Institute, UMR CNRS 6183, 1 rue de la Noë, 44321 Nantes, France
² Institut Universitaire de France (IUF), France
³ Ecole Centrale de Nantes, GeM Institute, UMR CNRS 6183, 1 rue de la Noë, 44321 Nantes, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Nicolas Mo\"es and Nicolas Chevaugeon},
     title = {Lipschitz regularization for softening material models: the {Lip-field} approach},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {415--434},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {349},
     number = {2},
     year = {2021},
     doi = {10.5802/crmeca.91},
     language = {en},
}

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Nicolas Moës; Nicolas Chevaugeon. Lipschitz regularization for softening material models: the Lip-field approach. Comptes Rendus. Mécanique, Volume 349 (2021) no. 2, pp. 415-434. doi : 10.5802/crmeca.91. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.91/

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