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REVIEW ARTICLES: Elastic Microstructures

Behavior of the Poisson Ratio of a Two-Phase Composite Material in the High-Concentration Limit

[+] Author and Article Information
Robert W. Zimmerman

Earth Sciences Division, Lawrence Berkeley Laboratory, University of California, Berkeley CA 94720

Appl. Mech. Rev 47(1S), S38-S44 (Jan 01, 1994) doi:10.1115/1.3122819 History: Online April 29, 2009

Abstract

The behavior of the Poisson ratio of a material filled with spherical inclusions is studied in the high-concentration limit, using the Mori-Tanaka and the differential effective medium theories. When the inclusions are either much stiffer or much softer than the matrix, both theories predict the existence of a boundary layer near c = 1 in the graph of the Poisson ratio ν as a function of inclusion concentration c. As c increases, ν first approaches some fixed point ν* that depends only on the matrix properties. In a localized region near c = 1, ν then varies rapidly so as to equal the Poisson ratio of the inclusions at c = 1. The results therefore show a qualitative distinction between, for example, the effect of very hard inclusions and infinitely rigid inclusions. The results also illustrate the extent to which the Poisson ratio fails to obey a mixing law of the Voigt or Reuss type, in that the effective Poisson ratio is not bounded between the Poisson ratios of the matrix and inclusion phases.

Copyright © 1994 by American Society of Mechanical Engineers
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