Comptes Rendus
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.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2004.04.004
Keywords: Computational solid mechanics, Homogenization, Composite materials, Nonlinear behavior
Mots-clés : Mécanique des solides numérique, Homogénéisation, Matériaux composites, Comportement non linéaire

Noël Lahellec 1; Pierre Suquet 1

1 Laboratoire de mécanique et d'acoustique, 31, chemin Joseph Aiguier, 13402 Marseille cedex 20, France
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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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[5] P. Ponte Castañeda; P. Suquet Nonlinear composites, Adv. Appl. Mech., vol. 34, Academic Press, New York, 1998, pp. 171-302

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