Comptes Rendus
no. 3
A micromechanics-based non-local anisotropic model for unilateral damage in brittle materials

Présenté par : Jean-Baptiste Leblond

Qi-zhi Zhu1  ; Jian-fu Shao1  ; Djimedo Kondo1
1 Laboratoire de mécanique de Lille-UMR CNRS 8107, Université de sciences et technologies Lille, cité scientifique, boulevard Paul-Langevin, 59655 Villeneuve d'Ascq cedex, France
Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 320-328.

La présente Note est dédiée à la formulation d'un modèle micromécanique non local d'endommagement anisotrope ainsi qu'à son application aux matériaux et structures en béton. Nous formulons d'abord un modèle local d'endommagement unilatéral anisotrope en se basant sur un schéma d'homogénéisation adapté qui prend en compte l'interaction entre les microfissures ainsi que leur distribution spatiale. La surface d'endommagement est construite à l'aide d'un critère basé sur le taux de restitution de l'énergie. Une extension non locale du modèle est ensuite proposée en remplaçant le taux de restitution de l'énergie local associée à chaque famille de microfissures par sa moyenne sur un volume caractéristique V du materiau centré au point matériel. Afin d'illustrer l'efficacité du modèle non local, en particulier l'indépendence de ces prédictions vis-à-vis du maillage, on présente quelques exemples concernant le processus de rupture de matériaux et structures en béton.

The present Note is devoted to the formulation of a micromechanics-based model of non-local anisotropic damage and its application to concrete materials and structures. We first formulate a local anisotropic unilateral damage model on the basis of a suitable homogenization scheme which takes into account interactions between penny-shaped microcracks as well as their spatial distribution. The damage surface is built by using an energy release rate-based criterion. Then a non-local extension of the model is proposed by replacing the local energy release-rate for each family of microcracks by its average over a characteristic volume V of the material centered at a given point. In order to demonstrate the efficiency of the non-local model in mesh-independent simulation of failure process in structures, some applications concerning failure of concrete materials and structures are presented.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2007.10.010
Keywords: Damage, Homogenization, Non-local damage, Induced anisotropy, Crack interactions, Unilateral effect
Mots clés : Endommagement, Homogénéisation, Endommagement non local, Anisotropie induite, Interaction entre fissures, Effets unilatéraux
Qi-zhi Zhu 1 ; Jian-fu Shao 1 ; Djimedo Kondo 1

1 Laboratoire de mécanique de Lille-UMR CNRS 8107, Université de sciences et technologies Lille, cité scientifique, boulevard Paul-Langevin, 59655 Villeneuve d'Ascq cedex, France 
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Qi-zhi Zhu; Jian-fu Shao; Djimedo Kondo. A micromechanics-based non-local anisotropic model for unilateral damage in brittle materials. Comptes Rendus. Mécanique, Volume 336 (2008) no. 3, pp. 320-328. doi : 10.1016/j.crme.2007.10.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.10.010/

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