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A Spherical Inclusion with Inhomogeneous Interface in Conduction

Published online by Cambridge University Press:  05 May 2011

T. Chen ,
C. H. Hsieh  and
P. C. Chuang
T. Chen*
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
C. H. Hsieh*
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
P. C. Chuang*
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
*Professor
**Graduate student
**Graduate student
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Abstract

A series solution is presented for a spherical inclusion embedded in an infinite matrix under a remotely applied uniform intensity. Particularly, the interface between the inclusion and the matrix is considered to be inhomegeneously bonded. We examine the axisymmetric case in which the interface parameter varies with the cone angle θ. Two kinds of imperfect interfaces are considered: an imperfect interface which models a thin interphase of low conductivity and an imperfect interface which models a thin interphase of high conductivity. We show that, by expanding the solutions of terms of Legendre polynomials, the field solution is governed by a linear set of algebraic equations with an infinite number of unknowns. The key step of the formulation relies on algebraic identities between coefficients of products of Legendre series. Some numerical illustrations are presented to show the correctness of the presented procedures. Further, solutions of the boundary-value problem are employed to estimate the effective conductivity tensor of a composite consisting of dispersions of spherical inclusions with equal size. The effective conductivity solely depends on one particular constant among an infinite number of unknowns.

Keywords

Inclusion problemsImperfect interfaceConduction
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 1 , March 2003 , pp. 1 - 8
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

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References

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