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


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
Your Session has timed out. Please sign back in to continue.





Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In