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Journal of Composite Materials
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The Effective Elastic Constants of Solids Containing Spherical Exclusions

John P. O'Rourke

Delphi Packard Electric Systems, Warren, OH 44484

Marc S. Ingber

Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131

Martin W. Weiser

Johnson Matthey Electronics, Spokane, WA 99019

This paper considers the effective elastic properties of solids containing random arrangements of spherical exclusions. The fully three-dimensional response of an elastic material containing voids undergoing a uniaxial tensile test is simulated using the boundary element method (BEM). The effective Young's modulus and the effective Poisson's ratio are calculated as a function of the void volume fraction by comparing numerical solutions of matrix materials with and without voids. Because these effective properties depend on the microstructure, scatter about a mean value is observed for an ensemble of random configurations of voids at a given volume fraction. The effect of the number of voids on the scatter is studied. To validate the numerical results, comparisons are made with analytic solutions and experimental results. Since the authors could fine no experimental results for the effective Poisson's ratio, experiments were conducted on porous rubber samples to confirm the numerical results.

Key Words: effective Young's modulus • effective Poisson's ratio • porous elastic materials • composites with random structure

Journal of Composite Materials, Vol. 31, No. 9, 910-934 (1997)
DOI: 10.1177/002199839703100905
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J. Y. Kim and B. J. Yoon
The Effective Conductivities of Composites with Cubic Arrays of Spheroids and Cubes
Journal of Composite Materials, July 1, 1999; 33(14): 1344 - 1362.
[Abstract] [PDF]