The solution to the generalized conduction Eshelby problem of a confocal N-layer spheroid with low or highly conducting interfaces between isotropic layers is provided thanks to a decomposition in series of harmonics. A generic workflow is detailed for practical numerical implementation including a fine analysis to assess the influence of the level of truncation of the infinite series. The case of perfect interfaces presents a particular interest insofar as it is characterized by an equivalent conductivity tensor obtained from a recursive procedure. The notion of equivalent conductivity is then investigated and applied to a uniform spheroid surrounded by an imperfect interface. Some approximated models are developed, either based on a surface description of the interface or on a thin interphase, casting a new light on published models and proposing a unified framework for new ones. These approximated models are finally analyzed by comparison to the exact solution.

由于一系列谐波的分解，提供了一种在各向同性层之间具有低或高导电界面的共焦N层球体的广义导电Eshelby问题的解决方案。详细的通用工作流程适用于实际的数值实现，包括精细分析以评估无限级数的截断水平的影响。理想界面的情况引起了特别的关注，因为它的特征在于从递归过程中获得的等效电导率张量。然后研究等效电导率的概念，并将其应用于由不完善界面包围的均匀球体。根据界面的表面描述或稀薄的相间相，开发了一些近似模型，为已发布的模型提供新的思路，并为新模型提出一个统一的框架。最后，通过与精确解进行比较来分析这些近似模型。