Within the framework of second-order gradient theory and the multi-scale modeling approach for periodic composite materials, a key challenge lies in determining the four tensors: $\mathbb{A}^{0,0}$, $\mathbb{B}^{0,1}$, $\mathbb{C}^{0,0}$, and $\mathbb{D}^{0,0}$, which appear in the asymptotic expansion of the energy. This paper presents the numerical evaluation and simulation of these tensors across various geometric configurations, employing a modified Green’s kernel-accelerated scheme to efficiently handle high-contrast cases. Extensive 3D simulations are conducted for multiple distinct geometries, accompanied by a detailed analysis of tensor values, computational efficiency, and classification. The results provide valuable insights into the behavior of these tensors across different morphological structures, contributing to a deeper understanding of advanced composite material modeling.
Dans le cadre de la théorie du gradient d’ordre deux et de l’approche de modélisation multi-échelle des matériaux composites périodiques, un défi majeur réside dans la détermination des quatre tenseurs : $\mathbb{A}^{0,0}$, $\mathbb{B}^{0,1}$, $\mathbb{C}^{0,0}$, et $\mathbb{D}^{0,0}$ qui apparaissent dans le développement asymptotique de l’énergie. Cet article présente l’évaluation numérique et la simulation de ces tenseurs pour différentes configurations géométriques, en utilisant un schéma modifié accéléré par le noyau de Green pour traiter efficacement les cas à fort contraste. De nombreuses simulations 3D sont menées pour plusieurs géométries distinctes, accompagnées d’une analyse détaillée des valeurs des tenseurs, de l’efficacité numérique et d’une classification. Les résultats fournissent des informations précieuses sur le comportement de ces tenseurs selon différentes structures morphologiques, contribuant ainsi à une meilleure compréhension de la modélisation avancée des matériaux composites.
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Mots-clés : Gradient d’ordre deux, fort contraste, matériaux composites périodiques, modélisation multi-échelle, simulation, FFT, FEM
Alioune Nacro 1; Philippe Karamian-Surville 1; Sophie Lemaitre 1
CC-BY 4.0
@article{CRMECA_2025__353_G1_815_0,
author = {Alioune Nacro and Philippe Karamian-Surville and Sophie Lemaitre},
title = {Multi-scale modeling and simulation of high-contrast periodic composite materials: second-order gradient theory},
journal = {Comptes Rendus. M\'ecanique},
pages = {815--862},
year = {2025},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
doi = {10.5802/crmeca.307},
language = {en},
}
TY - JOUR AU - Alioune Nacro AU - Philippe Karamian-Surville AU - Sophie Lemaitre TI - Multi-scale modeling and simulation of high-contrast periodic composite materials: second-order gradient theory JO - Comptes Rendus. Mécanique PY - 2025 SP - 815 EP - 862 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.307 LA - en ID - CRMECA_2025__353_G1_815_0 ER -
%0 Journal Article %A Alioune Nacro %A Philippe Karamian-Surville %A Sophie Lemaitre %T Multi-scale modeling and simulation of high-contrast periodic composite materials: second-order gradient theory %J Comptes Rendus. Mécanique %D 2025 %P 815-862 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.307 %G en %F CRMECA_2025__353_G1_815_0
Alioune Nacro; Philippe Karamian-Surville; Sophie Lemaitre. Multi-scale modeling and simulation of high-contrast periodic composite materials: second-order gradient theory. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 815-862. doi: 10.5802/crmeca.307
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