Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity

doi:10.1007/s10483-014-1831-9

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (7): 863-874.doi: https://doi.org/10.1007/s10483-014-1831-9

Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity

陈宜舟

Division of Engineering Mechanics, Jiangsu University, Zhenjiang 212013, Jiangsu Province, P. R. China

收稿日期:2013-06-16 修回日期:2013-12-20 出版日期:2014-07-01 发布日期:2014-07-01
通讯作者: Yi-zhou CHEN, Professor, Ph.D., E-mail:chens@ujs.edu.cn E-mail:chens@ujs.edu.cn

Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity

Yi-zhou CHEN

Division of Engineering Mechanics, Jiangsu University, Zhenjiang 212013, Jiangsu Province, P. R. China

Received:2013-06-16 Revised:2013-12-20 Online:2014-07-01 Published:2014-07-01

摘要/Abstract

摘要： This paper presents a closed form solution and numerical analysis for Eshelby's elliptic inclusion in an infinite plate. The complex variable method and the conformal mapping technique are used. The continuity conditions for the traction and displacement along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.

关键词: Eshelby’s elliptic inclusion, complex variable method, closed form solution

Abstract: This paper presents a closed form solution and numerical analysis for Eshelby's elliptic inclusion in an infinite plate. The complex variable method and the conformal mapping technique are used. The continuity conditions for the traction and displacement along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time.

Key words: Eshelby’s elliptic inclusion, complex variable method, closed form solution

中图分类号:

陈宜舟. Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 863-874.

Yi-zhou CHEN. Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(7): 863-874.

参考文献

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Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity

Closed form solution and numerical analysis for Eshelby’s elliptic inclusion in plane elasticity

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