title: Eshelby's problem of a spherical inclusion eccentrically embedded in a finite spherical body.
abstract: Resorting to the superposition principle, the solution of Eshelby's problem of a spherical inclusion located eccentrically inside a finite spherical domain is obtained in two steps: (i) the solution to the problem of a spherical inclusion in an infinite space; (ii) the solution to the auxiliary problem of the corresponding finite spherical domain subjected to appropriate boundary conditions. Moreover, a set of functions called the sectional and harmonic deviators are proposed and developed to work out the auxiliary solution in a series form, including the displacement and Eshelby tensor fields. The analytical solutions are explicitly obtained and illustrated when the geometric and physical parameters and the boundary condition are specified.
authors.affiliation: Institute for Advanced Study, Nanchang University, Nanchang 330031, People's Republic of China; Laboratoire de Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 5 bd Descartes, 77454 Marne-la-Vallée, France.
authors.forename: W-N
authors.identifier: 0000-0001-8442-377X
authors.initials: WN
authors.lastname: Zou
authors.affiliation: Laboratoire de Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS , Université Paris-Est , 5 bd Descartes, 77454 Marne-la-Vallée , France.
authors.forename: Q-C
authors.initials: QC
authors.lastname: He
keywords: Eshelby's problem; finite body; inclusion; sectional and harmonic deviator; superposition principle