On the non-conservativeness of a class of anisotropic damage models with unilateral effects

Noël Challamel; Damien Halm; André Dragon

doi:10.1016/j.crme.2006.05.006

On the non-conservativeness of a class of anisotropic damage models with unilateral effects
[Sur le caractère non-conservatif de quelques modèles d'endommagement anisotrope avec conditions unilatérales]

Présenté par : André Zaoui

Noël Challamel ¹ ; Damien Halm ² ; André Dragon ²

¹ Laboratoire de génie civil et génie mécanique, INSA Rennes, 20, avenue des Buttes de Coësmes, 35043 Rennes cedex, France
² Laboratoire de mécanique et de physique des matériaux (UMR CNRS 6617), ENSMA, BP 40109, 86961 Futuroscope Chasseneuil cedex, France

Comptes Rendus. Mécanique, Volume 334 (2006) no. 7, pp. 414-418.

Résumé
Abstract

L'objectif de cette note est de montrer qu'une classe de modèles élastique-endommageables anisotropes avec prise en compte spécifique des effets unilatéraux représente en réalité, à endommagement constant, une forme d'élasticité non-linéaire non-conservative. Le caractère conservatif (existence du potentiel thermodynamique) est équivalent à la symétrie du tenseur Hessien. On montre alors que, pour la classe de modèles considérés, la condition de conservation de l'énergie n'est assurée que lorsque les directions principales des tenseurs d'endommagement et de déformation coïncident (coaxialité au sens du dommage).

The aim of this Note is to show that a class of anisotropic elastic-damage models including unilateral effects can be considered, for constant damage values, as non-linear and non-conservative elastic. The conservative character of corresponding constitutive models is related to the symmetry of the Hessian tensor. For the models under consideration, it is shown that the condition of conservativeness (existence of the elastic potential energy function) is obtained only when there is coaxiality of the strain and damage tensors.

Reçu le : 2006-01-24
Accepté le : 2006-05-23
Publié le : 2006-06-30

DOI : 10.1016/j.crme.2006.05.006

Keywords: Damage, Non-linear elasticity, Tensorial damage, Unilateral effect, Non-conservative system, Hessian
Mot clés : Endommagement, Elasticité non-linéaire, Endommagement tensoriel, Effet unilatéral, Systeme non conservatif, Hessien

Affiliations des auteurs :

Noël Challamel ¹ ; Damien Halm ² ; André Dragon ²

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     title = {On the non-conservativeness of a class of anisotropic damage models with unilateral effects},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {414--418},
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     language = {en},
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Noël Challamel; Damien Halm; André Dragon. On the non-conservativeness of a class of anisotropic damage models with unilateral effects. Comptes Rendus. Mécanique, Volume 334 (2006) no. 7, pp. 414-418. doi : 10.1016/j.crme.2006.05.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.05.006/

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