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

Claude Stolz

doi:10.5802/crmeca.237

Article de recherche

On bounds of the effective behavior of particulate composites with imperfect interface
[Sur l’encadrement du comportement effectif des composites particulaires avec interface imparfaite]

Claude Stolz ¹

¹ IMSIA- CNRS-UMR 9219

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

Résumé
Abstract

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.

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.

Reçu le : 2023-05-22
Accepté le : 2024-01-11
Publié le : 2024-03-14

DOI : 10.5802/crmeca.237

Keywords: Composites, Imperfect interfaces, Bounding
Mot clés : Composites, interfaces imparfaites, encadrement, bornes

Affiliations des auteurs :

Claude Stolz ¹

¹ IMSIA- CNRS-UMR 9219

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     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/

Bibliographie
Cité par

[1] Z. Hashin; S. Shtrikman A variational approach to the theory of the elastic behaviour of multiphase materials, J. Mech. Phys. Solids, Volume 11 (1963), pp. 127-140 | DOI | MR | Zbl

[2] J. R. Willis Bounds and self-consistent estimates for the overall properties of anisotropic composites, J. Mech. Phys. Solids, Volume 25 (1977), pp. 185-202 | DOI | Zbl

[3] J. R. Willis Variational and related methods for the overall properties of composites, Adv. Appl. Mech., Volume 21 (1981), pp. 1-78 | DOI | MR | Zbl

[4] L. Walpole On bounds for the overall elastic moduli of inhomogeneous systems—I, J. Mech. Phys. Solids, Volume 14 (1966), pp. 151-162 | DOI | Zbl

[5] S. T. Gu; Q. C. He Interfacial discontinuity relations for coupled multifield phenomena and their application to the modeling of thin interphases as imperfect interfaces, J. Mech. Phys. Solids, Volume 59 (2011) no. 7, pp. 1413-1426 | DOI | MR | Zbl

[6] Y. Benveniste; T. Miloh Imperfect soft and stiff interfaces in two-dimensional elasticity, Mech. Mater., Volume 33 (2001), pp. 309-323 | DOI

[7] E. Hervé-Luanco Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites, Int. J. Solids Struct., Volume 51 (2014) no. 15-16, pp. 2865-2877 | DOI | Zbl

[8] Z. Hashin Thermoelastic properties of particulate composites with imperfect interface, J. Mech. Phys. Solids, Volume 39 (1991) no. 6, pp. 745-762 | DOI | MR

[9] L. Wu Bounds on the effective thermal conductivity of composites with imperfect interface, Int. J. Eng. Sci., Volume 48 (2010) no. 9, pp. 783-794 | DOI | Zbl

[10] S. Firooz; G. Chatzigeorgiou; P. Steinmann; A. Javili Extended general interfaces: Mori-–Tanaka homogenization and average fields, Int. J. Solids Struct., Volume 254-255 (2022), 111933 | DOI

[11] C. Stolz; A. Zaoui Combined variational approach and morphological analysis to the behaviour of inhomogeneous elastic media, C. R. Acad. Sci., Sér. IIA Earth Planet. Sci., Volume 312 (1991) no. 3, pp. 143-150 | Zbl

[12] M. Bornert; C. Stolz; A. Zaoui Morphologically representative pattern-based bounding in elasticity, J. Mech. Phys. Solids, Volume 44 (1996) no. 3, pp. 307-331 | DOI | MR | Zbl

[13] S. Brisard; L. Dormieux; D. Kondo Hashin–-Shtrikman bounds on the bulk modulus of a nanocomposite with spherical inclusions and interface effects, Comput. Mater. Sci., Volume 48 (2010), pp. 589-596 | DOI

[14] S. Brisard; L. Dormieux; D. Kondo Hashin–Shtrikman bounds on the shear modulus of a nanocomposite with spherical inclusions and interface effects, Comput. Mater. Sci., Volume 50 (2010), pp. 403-410 | DOI | Zbl

[15] H. Duan; J. Wang; Z. Huang; B. Karihaloo Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress, J. Mech. Phys. Solids, Volume 53 (2005) no. 7, pp. 1574-1596 | DOI | MR | Zbl

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