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Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites

Abstract : A stress-gradient material model was recently proposed by Forest and Sab [Mech. Res. Comm. 40, 16--25, 2012] as an alternative to the well-known strain-gradient model introduced in the mid 60s. We propose a theoretical framework for the homogenization of stress-gradient materials. We derive suitable boundary conditions ensuring that Hill–Mandel's lemma holds. As a first result, we show that stress-gradient materials exhibit a softening size-effect (to be defined more precisely in this paper), while strain-gradient materials exhibit a stiffening size-effect. This demonstrates that the stress-gradient and strain-gradient models are not equivalent as intuition would have it, but rather complementary. Using the solution to Eshelby's spherical inhomogeneity problem that we derive in this paper, we propose Mori–Tanaka estimates of the effective properties of stress-gradient composites with spherical inclusions, thus opening the way to more advanced multi-scale analyses of stress-gradient materials.
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Contributeur : Sébastien Brisard <>
Soumis le : jeudi 22 mars 2018 - 12:18:16
Dernière modification le : jeudi 1 juillet 2021 - 06:18:07
Archivage à long terme le : : jeudi 13 septembre 2018 - 05:30:31


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NOTICE: this is the author's version of a work that was accepted for publication in International Journal of Solids and Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Solids and Structures ( ).



V.P. Tran, Sébastien Brisard, Johann Guilleminot, Karam Sab. Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites. International Journal of Solids and Structures, Elsevier, 2018, 146, pp.55-68. ⟨10.1016/j.ijsolstr.2018.03.020⟩. ⟨hal-01740741v1⟩



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