TY - JOUR
T1 - A spherical inclusion with inhomogeneous interface in conduction
AU - Chen, Tungyang
AU - Hsieh, C. H.
AU - Chuang, P. C.
PY - 2003/1/1
Y1 - 2003/1/1
N2 - 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 6. 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.
AB - 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 6. 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.
UR - http://www.scopus.com/inward/record.url?scp=0042282708&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0042282708&partnerID=8YFLogxK
U2 - 10.1017/S1727719100004135
DO - 10.1017/S1727719100004135
M3 - Article
AN - SCOPUS:0042282708
SN - 1727-7191
VL - 19
SP - 1
EP - 8
JO - Journal of Mechanics
JF - Journal of Mechanics
IS - 1
ER -