Research Papers

A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion

[+] Author and Article Information
Xiaoqing Jin, Qian Wang

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208

Leon M. Keer

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208l-keer@northwestern.edu

J. Appl. Mech 78(3), 031009 (Feb 15, 2011) (6 pages) doi:10.1115/1.4003238 History: Received September 10, 2010; Revised December 08, 2010; Posted December 13, 2010; Published February 15, 2011; Online February 15, 2011

From the analytical formulation developed by Ju and Sun [1999, “A Novel Formulation for the Exterior-Point Eshelby’s Tensor of an Ellipsoidal Inclusion,” ASME Trans. J. Appl. Mech., 66, pp. 570–574], it is seen that the exterior point Eshelby tensor for an ellipsoid inclusion possesses a minor symmetry. The solution to an elliptic cylindrical inclusion may be obtained as a special case of Ju and Sun’s solution. It is noted that the closed-form expression for the exterior-point Eshelby tensor by Kim and Lee [2010, “Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion,” ASME Trans. J. Appl. Mech., 77, p. 024503] violates the minor symmetry. Due to the importance of the solution in micromechanics-based analysis and plane-elasticity-related problems, in this work, the explicit analytical solution is rederived. Furthermore, the exterior-point Eshelby tensor is used to derive the explicit closed-form solution for the elastic field outside the inclusion, as well as to quantify the elastic field discontinuity across the interface. A benchmark problem is used to demonstrate a valuable application of the present solution in implementing the equivalent inclusion method.

Copyright © 2011 by American Society of Mechanical Engineers
Topics: Tensors
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Grahic Jump Location
Figure 2

A plane strain elliptical cavity subjected to a remote uniform isotropic loading

Grahic Jump Location
Figure 1

Schematic illustration of an ellipsoidal inclusion, the imaginary ellipsoid, and its outward unit normal vector n⃑



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