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RESEARCH PAPERS

Two New Universal Relations in Nonlinear Elasticity and Some Related Matters

[+] Author and Article Information
M. Aron

School of Mathematics and Statistics, University of Plymouth, Drake Circus, Plymouth PL4 8AA, U.K.

S. Aizicovici

Department of Mathematics, Ohio University, Athens, OH 45701-2979

J. Appl. Mech 61(4), 784-787 (Dec 01, 1994) (4 pages) doi:10.1115/1.2901555 History: Received October 23, 1992; Revised August 06, 1993; Online March 31, 2008

Abstract

Two inequalities which for certain deformation classes may be viewed as universal relations are shown to hold for two distinct subclasses of unconstrained rubberlike solids. The inequalities express the fact that the mean stress corresponding to any purely distortional deformation originating from a given ground state is dominated by (and, respectively, dominates) the mean stress in that ground state. Also discussed is a case in which the deformations involved are necessarily homogeneous.

Copyright © 1994 by The American Society of Mechanical Engineers
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