Variational modeling adapted to the medium with gradient properties

Azdine Nait-Ali; Sami Ben Elhaj Salah

doi:10.5802/crmeca.254

Research article

Variational modeling adapted to the medium with gradient properties

Azdine Nait-Ali ¹ ; Sami Ben Elhaj Salah ¹

¹ Institut Pprime -UPR CNRS 3346 - Département Physique et Mécanique des Matériaux ENSMA - Téléport 2, 1er avenue Clément Ader BP 40109 F86961 Futuroscope Chasseneuil Cedex France

Comptes Rendus. Mécanique, Volume 352 (2024), pp. 159-168.

Abstract
Résumé

This study aims to develop a numerical homogenization method that can be applied to a heterogeneous stratified medium. Traditional scale transition methods are inadequate in capturing the essential gradient properties of some materials. Therefore, the focus of this work is to construct a homogenized model that considers the material property gradient. To achieve this, a two-step homogenization scheme is proposed. Firstly, the 3D model is decomposed into multiple 2D heterogeneous layers, and the behavior of each layer is estimated using a micro-mechanical model such as the Hashin–Shtrikman bounds. Secondly, a variational sum method is used to rebuild the behavior of the 3D environment. Finally, the method is applied to homogenize a thin plate with a porosity gradient.

Cette étude vise à développer une méthode d’homogénéisation numérique qui peut être appliquée à un milieu stratifié hétérogène. Les méthodes traditionnelles de transition d’échelle sont inadéquates pour capturer les propriétés essentielles de gradient de certains matériaux. Par conséquent, l’objectif de ce travail est de construire un modèle homogénéisé qui prenne en compte le gradient des propriétés du matériau. Pour ce faire, un schéma d’homogénéisation en deux étapes est proposé. Tout d’abord, le modèle 3D est décomposé en plusieurs couches hétérogènes 2D et le comportement de chaque couche est estimé à l’aide d’un modèle micromécanique tel que les bornes de Hashin–Shtrikman. Ensuite, une méthode de somme variationnelle est utilisée pour reconstruire le comportement de l’environnement 3D. Enfin, la méthode est appliquée à l’homogénéisation d’une plaque mince avec un gradient de porosité.

Received: 2023-11-21
Accepted: 2024-05-21
Published online: 2024-06-07

DOI: 10.5802/crmeca.254

Author's affiliations:

Azdine Nait-Ali ¹; Sami Ben Elhaj Salah ¹

¹ Institut Pprime -UPR CNRS 3346 - Département Physique et Mécanique des Matériaux ENSMA - Téléport 2, 1er avenue Clément Ader BP 40109 F86961 Futuroscope Chasseneuil Cedex France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

@article{CRMECA_2024__352_G1_159_0,
     author = {Azdine Nait-Ali and Sami Ben Elhaj Salah},
     title = {Variational modeling adapted to the medium with gradient properties},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {159--168},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {352},
     year = {2024},
     doi = {10.5802/crmeca.254},
     language = {en},
}

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Azdine Nait-Ali; Sami Ben Elhaj Salah. Variational modeling adapted to the medium with gradient properties. Comptes Rendus. Mécanique, Volume 352 (2024), pp. 159-168. doi : 10.5802/crmeca.254. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.254/

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