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

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:146

Article

Tran, V. P.^1,2  Brisard, S.¹  Guilleminot, J.³  Sab, K.¹ 

[1] Univ Paris Est, Lab Navier, ENPC, IFSTTAR,CNRS UMR 8205, 6 & 8 Ave Blaise Pascal, F-77455 Marne La Vallee 2, France

[2] Univ Paris Est, Lab Modelisat & Simulat Multi Echelie, CNRS, MSME UMR 8208, 5 Blvd Descartes,Champs Sur Marne, F-77454 Marne La Vallee, France

[3] Duke Univ, Dept Civil & Environm Engn, Durham, NC 27708 USA

关键词: Boundary conditions;    Elasticity;    Homogenization;    Inhomogeneity;    Micromechanics;    Stress-gradient;   

DOI  :  10.1016/j.ijsolstr.2018.03.020

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Ltd. All rights reserved.

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