Mori–Tanaka estimates of the effective elastic properties of stress-gradient composites. (1st August 2018)

• Record Type: Journal Article
• Authors: Tran, V.P.; Brisard, S.; Guilleminot, J.; Sab, K.
• Is Part Of: International journal of solids and structures. Volume 146(2018)
• Page Start: 55
• Page End: 68
• Publication Date: 2018-08-01
• Subjects: Boundary conditions -- Elasticity -- Homogenization -- Inhomogeneity -- Micromechanics -- Stress-gradient,; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2018.03.020
• Languages: English
• ISSNs: 0020-7683

Abstract

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.