[Composites non linéaires : un schéma exact au second ordre pour lequel la formulation en énergie de déformation coı̈ncide avec la formulation affine]
Cette Note présente une nouvelle approximation pour l'homogénéisation de composites non linéaires. Cette approximation préserve certaines qualités de la méthode du second ordre de Ponte Castañeda, qui sont l'exactitude au second ordre par rapport au constraste des phases et l'existence d'une énergie effective, mais corrige l'un de ses défauts qui est l'écart entre la méthode de l'énergie et la méthode affine. Un exemple numérique où des résultats exacts sont comparés aux résultats de l'approximation proposée, montre la précision de l'approche.
This Note presents a new approximate scheme for nonlinear composites. The approximation which is made preserves certain features of the original second-order scheme of Ponte Castañeda, exactness to second-order in the contrast and existence of an effective energy, but improves on one drawback, which is the gap between the strain-energy formulation and the affine formulation. A numerical example shows the accuracy of the present method.
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Mot clés : Mécanique des solides numérique, Homogénéisation, Matériaux composites, Comportement non linéaire
@article{CRMECA_2004__332_9_693_0,
author = {No\"el Lahellec and Pierre Suquet},
title = {Nonlinear composites: a linearization procedure, exact to second-order in contrast and for which the strain-energy and affine formulations coincide},
journal = {Comptes Rendus. M\'ecanique},
pages = {693--700},
publisher = {Elsevier},
volume = {332},
number = {9},
year = {2004},
doi = {10.1016/j.crme.2004.04.004},
language = {en},
}
TY - JOUR AU - Noël Lahellec AU - Pierre Suquet TI - Nonlinear composites: a linearization procedure, exact to second-order in contrast and for which the strain-energy and affine formulations coincide JO - Comptes Rendus. Mécanique PY - 2004 SP - 693 EP - 700 VL - 332 IS - 9 PB - Elsevier DO - 10.1016/j.crme.2004.04.004 LA - en ID - CRMECA_2004__332_9_693_0 ER -
%0 Journal Article %A Noël Lahellec %A Pierre Suquet %T Nonlinear composites: a linearization procedure, exact to second-order in contrast and for which the strain-energy and affine formulations coincide %J Comptes Rendus. Mécanique %D 2004 %P 693-700 %V 332 %N 9 %I Elsevier %R 10.1016/j.crme.2004.04.004 %G en %F CRMECA_2004__332_9_693_0
Noël Lahellec; Pierre Suquet. Nonlinear composites: a linearization procedure, exact to second-order in contrast and for which the strain-energy and affine formulations coincide. Comptes Rendus. Mécanique, Volume 332 (2004) no. 9, pp. 693-700. doi : 10.1016/j.crme.2004.04.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.04.004/
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