We consider the problem of determining the elastic field in an infinite elastic solid induced by an ellipsoidal inclusion with a distribution of eigenstrains. The particular type of distribution considered in the article is characterized by a polynomial in the Cartesian coordinates of the points of the inclusion. Eshelby showed that in such a situation the induced strain field within the inclusion is also characterized by a polynomial of the same order. However, the explicit expression for this polynomial seems to have not yet been reported in the literature. The present study fills this gap.
The Isotropic Ellipsoidal Inclusion With a Polynomial Distribution of Eigenstrain
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, June 5, 2001; final revision, Dec. 10, 2001. Associate Editor: D. A. Kouris. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Department of Mechanical and Environmental Engineering University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Rahman, M. (August 16, 2002). "The Isotropic Ellipsoidal Inclusion With a Polynomial Distribution of Eigenstrain ." ASME. J. Appl. Mech. September 2002; 69(5): 593–601. https://doi.org/10.1115/1.1491270
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