Journal
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
Volume 50, Issue 24, Pages 4010-4019Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2013.08.014
Keywords
Second-order homogenization; Higher-order elasticity; Effective non-local continuum; Characteristic length-scale; Composite materials
Categories
Funding
- Italian Prin [2009XWLFKW-002]
- [PIAP-GA-2011-286110-INTERCER2]
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It is shown that second-order homogenization of a Cauchy-elastic dilute suspension of randomly distributed inclusions yields an equivalent second gradient (Mindlin) elastic material. This result is valid for both plane and three-dimensional problems and extends earlier findings by Bigoni and Drugan [Bigoni, D., Drugan, W.J., 2007. Analytical derivation of Cosserat moduli via homogenization of heterogeneous elastic materials. J. Appl. Mech. 74, 741-753] from several points of view: (i) the result holds for anisotropic phases with spherical or circular ellipsoid of inertia; (ii) the displacement boundary conditions considered in the homogenization procedure is independent of the characteristics of the material; (iii) a perfect energy match is found between heterogeneous and equivalent materials (instead of an optimal bound). The constitutive higher-order tensor defining the equivalent Mindlin solid is given in a surprisingly simple formula. Applications, treatment of material symmetries and positive definiteness of the effective higher-order constitutive tensor are deferred to Part II of the present article. (C) 2013 Elsevier Ltd. All rights reserved.
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