On bounds of the effective behavior of particulate composites with imperfect interface

Claude Stolz

doi:10.5802/crmeca.237

Research article

On bounds of the effective behavior of particulate composites with imperfect interface

Claude Stolz ¹

¹ IMSIA- CNRS-UMR 9219

Comptes Rendus. Mécanique, Volume 352 (2024), pp. 39-54.

Abstract
Résumé

Particulate composites are considered here as multiphase composite in which the interfaces are imperfect. When the interface mechanical properties are those of a linear elastic material, the minimum of potential and complementary energy is used in order to obtain bounds of effective elastic modulus of the composite. Test displacements or stress fields are build and characterized using Green’s functions of a comparison homogeneous body, polarization fields and extension of the classical Lippmann–Schwinger equations. Then when spatial distribution of phases are known, in particular for isotropic distribution of phases or patterns, a generalization of Hashin–Shtrikman principle is obtained and lower and upper bounds are proposed.

Les composites particulaires sont composés d’une matrice à renforts particulaires, dans cette note les interfaces entre phases sont considérées imparfaites. Lorsque les propriétés mécaniques de l’interface sont celles d’un matériau élastique linéaire, les principes de minimum de l’énergie potentielle ou complémentaire sont utilisés afin d’obtenir des bornes sur les modules effectifs d’élasticité du composite. Des champs de déplacements ou des champs de contrainte admissibles sont construits et caractérisés à l’aide des fonctions de Green d’un corps homogène de comparaison, utilisant des champs de polarisation et une extension des équations classiques de Lippmann–Schwinger à des champs discontinus. Ensuite, lorsque la distribution spatiale des phases est connue, en particulier pour une distribution isotrope des phases ou des motifs, une généralisation du principe de Hashin–Shtrikman est obtenue et des bornes inférieures et supérieures du comportement effectif sont proposées.

Received: 2023-05-22
Accepted: 2024-01-11
Published online: 2024-03-14

DOI: 10.5802/crmeca.237

Keywords: Composites, Imperfect interfaces, Bounding
Mots-clés : Composites, interfaces imparfaites, encadrement, bornes

Author's affiliations:

Claude Stolz ¹

¹ IMSIA- CNRS-UMR 9219

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Claude Stolz},
     title = {On bounds of the effective behavior of particulate composites with imperfect interface},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {39--54},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {352},
     year = {2024},
     doi = {10.5802/crmeca.237},
     language = {en},
}

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Claude Stolz. On bounds of the effective behavior of particulate composites with imperfect interface. Comptes Rendus. Mécanique, Volume 352 (2024), pp. 39-54. doi : 10.5802/crmeca.237. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.237/

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