On the Extreme Values of Young’s Modulus, the Shear Modulus, and Poisson’s Ratio for Cubic Materials

[+] Author and Article Information
M. Hayes, A. Shuvalov

Department of Mathematical Physics, University College Dublin, Belfield, Dublin 4, Ireland

J. Appl. Mech 65(3), 786-787 (Sep 01, 1998) (2 pages) doi:10.1115/1.2789130 History: Received July 30, 1997; Revised May 04, 1998; Online October 25, 2007


For homogeneous cubic elastic materials with positive definite stored energy it is shown that the maximum and minimum values of Young’s modulus E are related to the maximum and minimum values of the shear modulus G through the simple connection 1/Gmin − 1/Gmax = 3(1/Emin − 1/Emax). It is deduced that the ratio of compliances −s12/s44 is the maximum value of Poisson’s ratio v in the cubic materials with a positive parameter χ = 2s11 − 2s12 − s44, and the minimum value of ν in the cubic materials with negative χ.

Copyright © 1998 by The American Society of Mechanical Engineers
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