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Technical Brief

On the Displacement of a Two-Dimensional Eshelby Inclusion of Elliptic Cylindrical Shape

[+] Author and Article Information
Xiaoqing Jin

State Key Laboratory of Mechanical Transmissions,
Chongqing University,
Chongqing 400030, China
e-mail: jinxq@cqu.edu.cn

Xiangning Zhang, Pu Li, Zheng Xu, Yumei Hu

State Key Laboratory of Mechanical Transmissions,
Chongqing University,
Chongqing 400030, China

Leon M. Keer

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

1Corresponding author.

2Jin et al., 2011, “A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion,” ASME J. Appl. Mech., 78(3), p. 031009.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 24, 2017; final manuscript received May 20, 2017; published online June 7, 2017. Assoc. Editor: M Taher A Saif.

J. Appl. Mech 84(7), 074501 (Jun 07, 2017) (6 pages) Paper No: JAM-17-1217; doi: 10.1115/1.4036820 History: Received April 24, 2017; Revised May 20, 2017

In a companion paper,ff2 we have obtained the closed-form solutions to the stress and strain fields of a two-dimensional Eshelby inclusion. The current work is concerned with the complementary formulation of the displacement. All the formulae are derived in explicit closed-form, based on the degenerate case of a three-dimensional (3D) ellipsoidal inclusion. A benchmark example is provided to validate the present analytical solutions. In conjunction with our previous study, a complete elasticity solution to the classical elliptic cylindrical inclusion is hence documented in Cartesian coordinates for the convenience of engineering applications.

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Copyright © 2017 by ASME
Topics: Tensors , Displacement
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Figures

Grahic Jump Location
Fig. 1

Schematic illustration of a confocal imaginary ellipsoid with its outward unit normal vector at x denoted by n⇀

Grahic Jump Location
Fig. 2

A plane strain elliptical cavity subjected to a remote uniform loading

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