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An algorithm for computing the effective linear elastic
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