On Hashin–Shtrikman-type bounds for nonlinear conductors

Michaël Peigney

doi:10.1016/j.crme.2017.02.006

On Hashin–Shtrikman-type bounds for nonlinear conductors

Michaël Peigney ¹

¹ Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, École des ponts ParisTech, IFSTTAR, 77455 Marne-la-Vallée, France

Comptes Rendus. Mécanique, Volume 345 (2017) no. 5, pp. 353-361.

Abstract

For linear composite conductors, it is known that the celebrated Hashin–Shtrikman bounds can be recovered by the translation method. We investigate whether the same conclusion extends to nonlinear composites in two dimensions. To that purpose, we consider two-phase composites with perfectly conducting inclusions. In that case, explicit expressions of the various bounds considered can be obtained. The bounds provided by the translation method are compared with the nonlinear Hashin–Shtrikman-type bounds delivered by the Talbot–Willis (1985) [2] and the Ponte Castañeda (1991) [3] procedures.

Received: 2017-01-16
Accepted: 2017-02-28
Published online: 2017-03-18

DOI: 10.1016/j.crme.2017.02.006

Keywords: Composite materials, Nonlinear homogenization, Bounds, Translation method

Author's affiliations:

Michaël Peigney ¹

¹ Université Paris-Est, Laboratoire Navier (UMR 8205), CNRS, École des ponts ParisTech, IFSTTAR, 77455 Marne-la-Vallée, France

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     title = {On {Hashin{\textendash}Shtrikman-type} bounds for nonlinear conductors},
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Michaël Peigney. On Hashin–Shtrikman-type bounds for nonlinear conductors. Comptes Rendus. Mécanique, Volume 345 (2017) no. 5, pp. 353-361. doi : 10.1016/j.crme.2017.02.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.02.006/

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