EIGENTENSORS OF LINEAR ANISOTROPIC ELASTIC MATERIALS

1 January 1990

journal article
Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics

Vol. 43 (1) , 15-41
https://doi.org/10.1093/qjmam/43.1.15

Abstract

There are two eigentensors for a linear isotropic elastic material; one is the deviatoric second-rank tensor, and the other is a second-rank tensor proportional to the unit tensor and often called the spherical or hydrostatic part of the tensor. The eigentensors of isotropic elasticity have many properties of physical and mathe-matical significance. In this paper a method of construction of the eigentensors for the anisotropic elastic-material symmetries is presented and applied to determine the eigentensors of each anisotropic elastic symmetry. The eigentensors for the anisotropic symmetries are shown to have the same important properties as those possessed by the eigentensors of isotropic elasticity.

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