REVIEW ARTICLES: Elastic Microstructures

Elastic Moduli of Composites With Random, Rigid Inclusions

[+] Author and Article Information
L. C. Davis, K. C. Hass

Scientific Research Laboratories, MD 3028, Ford Motor Company, Dearborn MI 48121-2053

J. Chen, M. F. Thorpe

Department of Physics and Astronomy and Center for Fundamental Materials Research, Michigan State University, East Lansing MI 48824

Appl. Mech. Rev 47(1S), S5-S9 (Jan 01, 1994) doi:10.1115/1.3122823 History: Online April 29, 2009


The elastic moduli of composite materials consisting of an isotropic, elastic matrix with perfectly rigid inclusions have been studied near random close packing. In two dimensional systems of uniform sized disks, the moduli have been determined by computer simulations. A theory of the bulk modulus k is developed by assuming that the elastic energy of the neck regions is minimized subject to the constraint that average local strain, <εi >, equals the macroscopic strain. Here the change in center-to-center distance to the ith nearest neighbor disk is δri =εi ri . We show that εi ∝ √ wi , where wi is the gap (ri −2R, R=disk radius). This prediction has been verified by the simulations, which also confirm our theory. Our findings appear to be the first example of local geometry dominating the strain near close packing. Predictions for the bulk modulus K in three dimensional systems of rigid spheres (radius = R) are also made. In this case, εi ∝ 1/log(R/wi ).

Copyright © 1994 by American Society of Mechanical Engineers
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