The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid

[+] Author and Article Information
Joseph F. Shelley

U. S. Merchant Marine Academy, Kings Point, N. Y.

Yi-Yuan Yu

Department of Mechanical Engineering, Polytechnic Institute of Brooklyn, Brooklyn, N. Y.

J. Appl. Mech 33(1), 68-74 (Mar 01, 1966) (7 pages) doi:10.1115/1.3625027 History: Received January 13, 1965; Online September 15, 2011


Presented in this paper is a solution in series form for the stresses in an infinite elastic solid which contains two rigid spherical inclusions of the same size. The stress field at infinity is assumed to be either hydrostatic tension or uniaxial tension in the direction of the common axis of the inclusions. The solution is based upon the Papkovich-Boussinesq displacement-function approach and makes use of the spherical dipolar harmonics developed by Sternberg and Sadowsky. The problem is closely related to, but turns out to be much more involved than, the corresponding problem of two spherical cavities solved by these authors.

Copyright © 1966 by ASME
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