Homogenization and Smoothing: A Unified View of Two Derivations of Effective Property Theories and Extensions

[+] Author and Article Information
L. Fishman, J. J. McCoy

The Catholic University of America, Washington, D.C. 20064

J. Appl. Mech 47(3), 679-682 (Sep 01, 1980) (4 pages) doi:10.1115/1.3153759 History: Received March 01, 1980; Revised April 01, 1980; Online July 21, 2009


The response of a continuum characterized by two widely differing length scales, parameterized by the dimensionless ratio ε, is considered in the context of the composite materials problem. The development of a bulk property theory appropriate in the ε → 0 limit is examined, both from the perspective of the deterministic homogenization literature and the smoothing method associated with statistical continuum theory, and a unified framework is established. The extension of bulk property theories through the development of ordered expansions in powers of ε is discussed and specifically related to analogous treatments in linear-gas relaxation theory.

Copyright © 1980 by ASME
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