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RESEARCH PAPERS

The Proportional Anisotropic Elastic Invariants

[+] Author and Article Information
A. M. Sadegh, S. C. Cowin

Department of Mechanical Engineering, City College of the City University of New York, New York, NY 10031

J. Appl. Mech 58(1), 50-57 (Mar 01, 1991) (8 pages) doi:10.1115/1.2897178 History: Received November 16, 1989; Revised May 07, 1990; Online March 31, 2008

Abstract

There are two proportional invariants for a linear isotropic material, the hydrostatic invariant, and the deviatoric invariant. The former is proportional to the trace of the tensor and the latter is proportional to the trace of the square of the associated deviatoric tensor. The hydrostatic stress and strain and the von Mises stress and strain are directly related to the hydrostatic and deviatoric proportional invariants, respectively, for an isotropic, linear elastic material. For each anisotropic linear elastic material symmetry there are up to six proportional invariants. In this paper we illustrate the six proportional invariants of an orthotropic elastic material using the elastic constants for spruce as the numerical example. The proportional elastic invariants play a role in anisotropic linear elasticity similar to the roles played by the hydrostatic stress and strain and the von Mises stress and strain in isotropic elasticity. They are the unique parameters whose contours represent both the stress and the strain distributions. They also have potential for representing failure or fracture criteria.

Copyright © 1991 by The American Society of Mechanical Engineers
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