Cross Relations Between the Planar Elastic Moduli of Perforated Structures

[+] Author and Article Information
Shmuel Vigdergauz

R&D Division,  The Israel Electric Corporation, Ltd., P. O. Box 10, Haifa 31000, Israelsmuel@iec.co.il

J. Appl. Mech 73(1), 163-166 (Nov 01, 2004) (4 pages) doi:10.1115/1.1938202 History: Received July 08, 2004; Revised November 01, 2004

The effective compliance moduli of a plate with a doubly periodic set of traction-free holes are considered. Attention is drawn to the perturbation form in which they are expressed by applying the complex variable methods in two-dimensional elasticity. This permits one to derive specific dimensionless combinations of the effective moduli, which are independent of the solid Poisson ratio. Using them saves computations of the structure moduli by FEM-like methods and helps one to evaluate their practical accuracy. Thus far, the only result of this kind has been observed numerically by Day, Snyder, Garboczi, and Thorpe (J. Mech. Phys. Solids.40, pp. 1031–1051, 1992) and later proved by Cherkaev, Lurie, and Milton (Proc. R. Soc. London, Ser. A458, pp. 519–529, 1992).

Copyright © 2006 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

The combined increment H1,2(c) from 24 in a square lattice: H1(c) for a square hole (1) and H1(c),H2(c) for the equistress hole (2 and 3, respectively). The dotted segments visually extrapolate the computed results up to the cellular limit c=1. The required dilute limits A0,B1,2016 are borrowed from 15.



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