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** Next:** Introduction

properties of heterogeneous materials: 3-D results for

composites with equal phase Poisson ratios

E.J. Garboczi

Building Materials Division

National Institute of Standards and Technology

Building 226, Room B348

Gaithersburg, Maryland 20899

A.R. Day

Marquette University

Department of Physics

Milwaukee, WI 53233

Abstract

An algorithm based on finite elements applied to digital images is described for computing the
linear elastic properties of heterogeneous materials. As an example of the algorithm, and for their
own intrinsic interest, the effective Poisson's ratio of two-phase random isotropic composites are
investigated numerically and via effective medium theory, in two and three dimensions. For the
specific case where both phases have the same Poisson's ratio
(_{1} = _{2}),
it is found that
there exists a critical value ^{*},
such that when
_{1} = _{2} >
^{*} ,
the composite
Poisson's ratio always decreases
when the two phases are mixed. If
_{1} = _{2} <
^{*} ,
the value of always increases when
the two phases are mixed. In d dimensions, the
value of ^{*} is predicted to be 1/(2d-1) using effective medium theory and scaling arguments.
Numerical results are presented in two and three dimensions that support this picture, which is
believed to be largely independent of microstructural details.

- Introduction
- Algorithms
- Effective Medium Theory
- Tests of elastic algorithm
- Numerical Results
- Discussion and Conclusions
- Acknowledgments
- References

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