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

Publication ,  Journal Article
Tran, VP; Brisard, S; Guilleminot, J; Sab, K
Published in: International Journal of Solids and Structures
August 1, 2018

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.

Duke Scholars

Published In

International Journal of Solids and Structures

DOI

ISSN

0020-7683

Publication Date

August 1, 2018

Volume

146

Start / End Page

55 / 68

Related Subject Headings

  • Mechanical Engineering & Transports
  • 40 Engineering
  • 09 Engineering
 

Citation

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Tran, V. P., Brisard, S., Guilleminot, J., & Sab, K. (2018). Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites. International Journal of Solids and Structures, 146, 55–68. https://doi.org/10.1016/j.ijsolstr.2018.03.020
Tran, V. P., S. Brisard, J. Guilleminot, and K. Sab. “Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites.” International Journal of Solids and Structures 146 (August 1, 2018): 55–68. https://doi.org/10.1016/j.ijsolstr.2018.03.020.
Tran VP, Brisard S, Guilleminot J, Sab K. Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites. International Journal of Solids and Structures. 2018 Aug 1;146:55–68.
Tran, V. P., et al. “Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites.” International Journal of Solids and Structures, vol. 146, Aug. 2018, pp. 55–68. Scopus, doi:10.1016/j.ijsolstr.2018.03.020.
Tran VP, Brisard S, Guilleminot J, Sab K. Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites. International Journal of Solids and Structures. 2018 Aug 1;146:55–68.
Journal cover image

Published In

International Journal of Solids and Structures

DOI

ISSN

0020-7683

Publication Date

August 1, 2018

Volume

146

Start / End Page

55 / 68

Related Subject Headings

  • Mechanical Engineering & Transports
  • 40 Engineering
  • 09 Engineering