Comptes Rendus
no. 12
Stochastic homogenization of reinforced polymer with very small carbon inclusions
Azdine Nait-ali1
1 Institut Pprime, UPR CNRS 3346, Département “Physique et mécanique des matériaux”, ENSMA, Téléport 2, 1, avenue Clément-Ader, BP 40109, 86961 Futuroscope Chasseneuil cedex, France
Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1192-1198.

In this study, we wish to determine a homogenized model of a material reinforced by spherical inclusion that is randomly distributed in space. The method used for the transition to the limit is Γ-convergence [1] in the stochastic case. In addition to the stochastic framework, the very small size compared to the characteristic size of the materials makes the homogenization procedure unconventional. In this study, we want to determine a homogenized model of a material reinforced by a spherical inclusion distributed randomly in space. The peculiarity here is that these particles are of very small size, this generating an energy due to the strong contrast of microstructure. The method used for the transition to the limit is Γ-convergence [1] in the stochastic case. The random distribution is taken into account during the transition of scales, so as to preserve the statistical information, and that in spite of the passage to the limit. In addition to the stochastic framework, the very small size compared to the characteristic size of the materials makes the homogenization procedure unconventional.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2018.09.002
Keywords: Asymptotic analysis, Γ-convergence, Ergodic theory

Azdine Nait-ali 1

1 Institut Pprime, UPR CNRS 3346, Département “Physique et mécanique des matériaux”, ENSMA, Téléport 2, 1, avenue Clément-Ader, BP 40109, 86961 Futuroscope Chasseneuil cedex, France 
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     title = {Stochastic homogenization of reinforced polymer with very small carbon inclusions},
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     doi = {10.1016/j.crme.2018.09.002},
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Azdine Nait-ali. Stochastic homogenization of reinforced polymer with very small carbon inclusions. Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1192-1198. doi : 10.1016/j.crme.2018.09.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.09.002/

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