Eigenfunctions at a Singular Point in Transversely Isotropic Materials Under Axisymmetric Deformations

[+] Author and Article Information
T. C. T. Ting, Yijian Jin

Department of Civil Engineering, Mechanics and Metallurgy, University of Illinois at Chicago, P.O. Box 4348, Chicago, Ill. 60680

S. C. Chou

U.S. Army Materials and Mechanics Research Center, Watertown, Mass. 02172

J. Appl. Mech 52(3), 565-570 (Sep 01, 1985) (6 pages) doi:10.1115/1.3169102 History: Received April 01, 1984; Online July 21, 2009


When a two-dimensional elastic body that contains a notch or a crack is under a plane stress or plane strain deformation, the asymptotic solution of the stress near the apex of the notch or crack is simply a series of eigenfunctions of the form ρδ f (ψ,δ) in which (ρ,ψ) is the polar coordinate with origin at the apex and δ is the eigenvalue. If the body is a three-dimensional elastic solid that contains axisymmetric notches or cracks and subjected to an axisymmetric deformation, the eigenfunctions associated with an eigenvalue contains not only the ρδ term, but also the ρδ +1 , ρδ+2 [[ellipsis]] terms. Therefore, the second and higher-order terms of the asymptotic solution are not simply the second and subsequent eigenfunctions. We present the eigenfunctions for transversely isotropic materials under an axisymmetric deformation. The degenerate case in which the eigenvalues p 1 and p 2 of the elasticity constants are identical is also considered. The latter includes the isotropic material as a special case.

Copyright © 1985 by ASME
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