4.5 Article

Eshelby's problem of a spherical inclusion eccentrically embedded in a finite spherical body

Publisher

ROYAL SOC
DOI: 10.1098/rspa.2016.0808

Keywords

Eshelby's problem; inclusion; finite body; superposition principle; sectional and harmonic deviator

Funding

  1. National Science Foundation of China (NSFC) [11372124]
  2. China Scholarship Council (CSC) [201506825048]

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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.

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