Zou W-N, He Q-C
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.
Laboratoire de Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS , Université Paris-Est , 5 bd Descartes, 77454 Marne-la-Vallée , France.
Proc Math Phys Eng Sci. 2017 Feb;473(2198):20160808. doi: 10.1098/rspa.2016.0808.
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.
借助叠加原理，通过两步得到了位于有限球形域内偏心球形夹杂的埃舍尔比问题的解：(i) 无限空间中球形夹杂问题的解；(ii) 对应有限球形域在适当边界条件下辅助问题的解。此外，还提出并发展了一组称为截面和调和偏差张量的函数，以将辅助解表示为级数形式，包括位移场和埃舍尔比张量场。当指定几何和物理参数以及边界条件时，明确地得到并给出了解析解。
