A Crack in a Confocal Elliptic Inhomogeneity Embedded in an Infinite Medium

[+] Author and Article Information
Chien H. Wu, Chao-Hsun Chen

Department of Civil Engineering, Mechanics, and Metallurgy, University of Illinois at Chicago, Chicago, IL 60680

J. Appl. Mech 57(1), 91-96 (Mar 01, 1990) (6 pages) doi:10.1115/1.2888330 History: Received November 04, 1988; Revised March 31, 1989; Online March 31, 2008


A family of confocal ellipses may be characterized by a single parameter, ρ> 1. In the limit as ρ→1, the ellipse degenerates into a straight line of length 2. It tends to a circle of infinite radius as ρ→ ∞. The geometry of the title problem is fixed by the crack (ρ = 1) and the size of an elliptic inhomogeneity (ρ = ρ0 ). Both the inhomogeneity and the infinite medium are assumed to be homogeneous and isotropic. Plane and anti-plane solutions associated with remote loading conditions are obtained. The solutions depend, among other parameters, on the size of the inhomogeneity ρ0 . Special attention is placed on determining the various limits as ρ0 →1.

Copyright © 1990 by The American Society of Mechanical Engineers
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