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REVIEW ARTICLES: Elastic Microstructures

Elastic Moduli of Two Dimensional Materials With Polygonal and Elliptical Holes

[+] Author and Article Information
I. Jasiuk

Department of Materials Science and Mechanics, Michigan State University, East Lansing MI 48824

J. Chen, M. F. Thorpe

Department of Physics and Astronomy, Michigan State University, East Lansing MI 48824

Appl. Mech. Rev 47(1S), S18-S28 (Jan 01, 1994) doi:10.1115/1.3122813 History: Online April 29, 2009

Abstract

We study the effective elastic moduli of two-dimensional composite materials containing polygonal holes. In the analysis we use a complex variable method of elasticity involving a conformal transformation. Then we take a far field result and derive the effective elastic constants of composites with a dilute concentration of polygonal holes. In the discussion we use the recently-stated Cherkaev-Lurie-Milton theorem, which gives general relations between the effective elastic constants of two-dimensional composites. We also discuss known results for elliptical holes in the context of the present work.

Copyright © 1994 by American Society of Mechanical Engineers
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