Vol. 8, No. 5-7, 2013

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ISSN: 1559-3959
Evaluation of the effective elastic moduli of particulate composites based on Maxwell’s concept of equivalent inhomogeneity: microstructure-induced anisotropy

Volodymyr I. Kushch, Sofia G. Mogilevskaya, Henryk K. Stolarski and Steven L. Crouch

Vol. 8 (2013), No. 5-7, 283–303
Abstract

Maxwell’s concept of equivalent inhomogeneity is employed for evaluating the effective elastic properties of macroscopically anisotropic particulate composites with isotropic phases. The effective anisotropic elastic properties of the material are obtained by comparing the far-field solutions for the problem of a finite cluster of isotropic particles embedded in an infinite isotropic matrix with those for the problem of a single anisotropic equivalent inhomogeneity embedded in the same matrix. The former solutions precisely account for the interactions between all particles in the cluster and for their geometrical arrangement. Illustrative examples involving periodic (simple cubic) and random composites suggest that the approach provides accurate estimates of their effective elastic moduli.

Keywords
Maxwell’s methodology, anisotropic elastic moduli, particulate composites, spherical particles, spherical harmonics
Milestones
Received: 21 November 2012
Revised: 26 March 2013
Accepted: 4 April 2013
Published: 18 November 2013
Authors
Volodymyr I. Kushch
Institute for Superhard Materials
National Academy of Sciences of Ukraine
2 Avtozavodskaya St.
Kiev 04074
Ukraine
Sofia G. Mogilevskaya
Department of Civil Engineering
University of Minnesota
500 Pillsbury Drive SE
Minneapolis, MN 55455
United States
http://www.ce.umn.edu/people/faculty/mogilevs/
Henryk K. Stolarski
Department of Civil Engineering
University of Minnesota
500 Pillsbury Drive SE
Minneapolis, MN 55455
United States
Steven L. Crouch
Department of Civil Engineering
University of Minnesota
500 Pillsbury Drive SE
Minneapolis, MN 55455
United States
http://www.ce.umn.edu/directory/faculty/crouch