Journal
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
Volume 78, Issue 3, Pages -Publisher
ASME
DOI: 10.1115/1.4003238
Keywords
inclusion; exterior field; exterior-point Eshelby tensor; micromechanics
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Funding
- Timken Co.
- U.S. Army TACOM
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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. [DOI: 10.1115/1.4003238]
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