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TECHNICAL PAPERS

Consistent Hashin-Shtrikman Bounds on the Effective Properties of Periodic Composite Materials

[+] Author and Article Information
P. Bisegna

University of Roma “Tor Vergata,” Department of Civil Engineering, 00133 Rome, Italy

R. Luciano

Department of Industrial Engineering, 03043 Cassino, Italy

J. Appl. Mech 66(4), 858-866 (Dec 01, 1999) (9 pages) doi:10.1115/1.2791789 History: Received July 30, 1996; Revised February 20, 1999; Online October 25, 2007

Abstract

In this paper the four classical Hashin-Shtrikman variational principles, applied to the homogenization problem for periodic composites with a nonlinear hyperelastic constitutive behavior, are analyzed. It is proved that two of them are indeed minimum principles while the other two are saddle point principles. As a consequence, every approximation of the former ones provide bounds on the effective properties of composite bodies, while approximations of the latter ones may supply inconsistent bounds, as it is shown by two numerical examples. Nevertheless, the approximations of the saddle point principles are expected to provide better estimates than the approximations of the minimum principles.

Copyright © 1999 by The American Society of Mechanical Engineers
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