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RESEARCH PAPERS

Nonlinear Elastic Properties of Micro-Heterogeneous Media

[+] Author and Article Information
E. Kröner

Institut für Theoretische und Angewandte Physik, der Universität Stuttgart und Max-Planck-Institut für Metallforschung, Stuttgart

J. Eng. Mater. Technol 116(3), 325-330 (Jul 01, 1994) (6 pages) doi:10.1115/1.2904295 History: Received August 15, 1993; Revised January 17, 1994; Online April 29, 2008

Abstract

Utilizing statistical methods known from linear elasticity it is shown how effective 3rd (and higher) order elastic constants (TOEC) of micro-heterogeneous media can be calculated. Emphasis is put on the self consistent scheme. The ensemble average of the fluctuating TOEC yields a 0th approximation to the rigorous selfconsistent moduli. A first approximation is also given in closed form. The insight that the well-established statistical methods of the linear theory, which uses Green functions, are applicable also to nonlinear problems is considered as the main result of this paper.

Copyright © 1994 by The American Society of Mechanical Engineers
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