On interfacial properties in gradient damaging continua

Ahmed Benallal; Claudia Comi

doi:10.1016/j.crme.2005.02.001

On interfacial properties in gradient damaging continua

Presented by: Évariste Sanchez-Palencia

Ahmed Benallal ¹; Claudia Comi ²

¹ Laboratoire de mécanique et technologie, ENS de Cachan/CNRS/université Paris 6, 61, avenue du Président Wilson, 94235 Cachan, France
² Department of Structural Engineering, Politecnico di Milano, Piazza L. da Vinci, 32, 20133 Milano, Italy

Comptes Rendus. Mécanique, Volume 333 (2005) no. 4, pp. 319-324.

Abstract
Résumé

The bifurcation problem near an interface is considered for a heterogeneous body made of two different materials that damage following gradient constitutive relations. The roles of internal length scales on bifurcation are studied especially in the shortwavelength regime. It is shown that the interfacial complementing condition is always satisfied meaning that a minimum wavelength exists for the bifurcation mode. The regularization properties of gradient damage models are underlined. A simple plane strain problem is used to illustrate the results. The interface bifurcated modes are explicitly computed: their wavelengths turn out to be fixed by the gradient coefficient; the influence of the interface behaviour is also highlighted.

Les phénomènes de bifurcation en présence d'interfaces sont analysés lorsque le comportement des matériaux constitutifs d'un solide hétérogène est gouverné par des modèles à gradient. Les roles des longueurs internes sont étudiés particulièrement aux faibles longueurs d'onde et on montre que la condition complémentaire aux interfaces est toujours satisfaite impliquant l'existence d'une longueur d'onde minimale pour le mode de bifurcation. Les effets régularisants sont soulignés et on illustre les résultats à l'aide d'un exemple en déformations planes où les modes de bifurcation sont explicitement calculés.

Received: 2004-02-18
Accepted: 2005-01-26
Published online: 2005-02-24

DOI: 10.1016/j.crme.2005.02.001

Keywords: Damage, Interface, Bifurcation
Mots-clés : Endommagement, Interface, Bifurcation

Author's affiliations:

Ahmed Benallal ¹; Claudia Comi ²

¹ Laboratoire de mécanique et technologie, ENS de Cachan/CNRS/université Paris 6, 61, avenue du Président Wilson, 94235 Cachan, France
² Department of Structural Engineering, Politecnico di Milano, Piazza L. da Vinci, 32, 20133 Milano, Italy

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     title = {On interfacial properties in gradient damaging continua},
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     pages = {319--324},
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     number = {4},
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     doi = {10.1016/j.crme.2005.02.001},
     language = {en},
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Ahmed Benallal; Claudia Comi. On interfacial properties in gradient damaging continua. Comptes Rendus. Mécanique, Volume 333 (2005) no. 4, pp. 319-324. doi : 10.1016/j.crme.2005.02.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.02.001/

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