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.
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e-mail: l-keer@northwestern.edu
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A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion
Xiaoqing Jin,
Xiaoqing Jin
Department of Mechanical Engineering,
Northwestern University
, Evanston, IL 60208
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Leon M. Keer,
Leon M. Keer
Department of Mechanical Engineering,
e-mail: l-keer@northwestern.edu
Northwestern University
, Evanston, IL 60208
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Qian Wang
Qian Wang
Department of Mechanical Engineering,
Northwestern University
, Evanston, IL 60208
Search for other works by this author on:
Xiaoqing Jin
Department of Mechanical Engineering,
Northwestern University
, Evanston, IL 60208
Leon M. Keer
Department of Mechanical Engineering,
Northwestern University
, Evanston, IL 60208e-mail: l-keer@northwestern.edu
Qian Wang
Department of Mechanical Engineering,
Northwestern University
, Evanston, IL 60208J. Appl. Mech. May 2011, 78(3): 031009 (6 pages)
Published Online: February 15, 2011
Article history
Received:
September 10, 2010
Revised:
December 8, 2010
Posted:
December 13, 2010
Published:
February 15, 2011
Online:
February 15, 2011
Citation
Jin, X., Keer, L. M., and Wang, Q. (February 15, 2011). "A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion." ASME. J. Appl. Mech. May 2011; 78(3): 031009. https://doi.org/10.1115/1.4003238
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