A dissipation-based control method for the multi-scale modelling of quasi-brittle materials

Thierry J. Massart; Ron H.J. Peerlings; Marc G.D. Geers

doi:10.1016/j.crme.2005.05.003

A dissipation-based control method for the multi-scale modelling of quasi-brittle materials
[Une méthode de contrôle basée sur la dissipation pour la modélisation multi-échelles des matériaux quasi-fragiles]

Présenté par : André Jaumotte

Thierry J. Massart ¹ ; Ron H.J. Peerlings ² ; Marc G.D. Geers ²

¹ Structural and Material Computational Mechanics Department CP 194/5, Université Libre de Bruxelles, avenue F.-D. Roosevelt 50, 1050 Brussels, Belgium
² Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

Comptes Rendus. Mécanique, Volume 333 (2005) no. 7, pp. 521-527.

Résumé
Abstract

Des schémas multi-échelles basés sur des principes d'homogénéisation numériques sont actuellement développés pour la simulation de comportements matériels complexes. L'utilisation de techniques d'homogénéisation sur des éléments de volume représentatifs de tailles finies en présence d'endommagement quasi-fragile peut causer l'apparition d'effets de snap-back dans la réponse matérielle macroscopique. Une méthode est proposée permettant d'introduire ce type de réponse dans un schéma multi-échelles, basée sur le contrôle de la dissipation à l'échelle mésoscopique.

Multi-scale models based on computational homogenisation are nowadays developed for the simulation of complex material behaviour. The use of homogenisation techniques on finite-sized representative volume elements in the presence of quasi-brittle damage may lead to the presence of snap-backs in the macroscopic material response. A methodology to simulate this type of response in the multi-scale technique is proposed, based on the control of the dissipation at the mesoscopic scale.

Reçu le : 2004-10-25
Accepté le : 2005-05-24
Publié le : 2005-06-23

DOI : 10.1016/j.crme.2005.05.003

Keywords: Computational solid mechanics, Multi-scale modelling, Localisation, Snap-back, Path following method, Dissipation control
Mots-clés : Mécanique des solides numérique, Modélisation multi-échelles, Localisation, Snap-back, Méthode de continuation, Contrôle par dissipation

Affiliations des auteurs :

Thierry J. Massart ¹ ; Ron H.J. Peerlings ² ; Marc G.D. Geers ²

¹ Structural and Material Computational Mechanics Department CP 194/5, Université Libre de Bruxelles, avenue F.-D. Roosevelt 50, 1050 Brussels, Belgium
² Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

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Thierry J. Massart; Ron H.J. Peerlings; Marc G.D. Geers. A dissipation-based control method for the multi-scale modelling of quasi-brittle materials. Comptes Rendus. Mécanique, Volume 333 (2005) no. 7, pp. 521-527. doi : 10.1016/j.crme.2005.05.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.05.003/

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