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The Stress Field Due to an Edge Dislocation Interacting With Two Circular Inclusions

Published online by Cambridge University Press:  14 July 2016

C.-K. Chao ,
F.-M. Chen  and
T.-H. Lin
C.-K. Chao*
Affiliation:
Department of Mechanical EngineeringNational Taiwan University of Science and TechnologyTaipei, Taiwan
F.-M. Chen
Affiliation:
Department of Mechanical EngineeringNan Kai University of TechnologyNantou, Taiwan
T.-H. Lin
Affiliation:
Department of Mechanical EngineeringNational Taiwan University of Science and TechnologyTaipei, Taiwan
*
*Corresponding author (ckchao@mail.ntust.edu.tw)
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Abstract

A general series solution to the problem of interacting circular inclusions in plane elastostatics is presented in this paper. The analysis is based on the use of the complex stress potentials of Muskhelishvili and the theorem of analytical continuation. The general forms of the complex potentials are derived explicitly for the circular inhomogeneities under arbitrary plane loading. Using the alternation technique, these general expressions were subsequently employed to treat the problem of an infinitely extended matrix containing two arbitrarily located inhomogeneities. The major contribution of the present proposed method is shown to be capable of yielding approximate closed-form solutions for multiple inclusions, thus providing the explicit dependence of the solution on the pertinent parameters. The result shows that the dislocation has a stable equilibrium position at a certain combination of material constants. The case of an inhomogeneity interacting with a circular hole under a remote uniform load is also investigated.

Keywords

Interacting circular inclusionsAnalytical continuationAlternation technique
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 2 , April 2017 , pp. 161 - 172
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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