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Article Dans Une Revue International Journal of Engineering Science Année : 2020

The Eshelby problem of the confocal N-layer spheroid with imperfect interfaces and the notion of equivalent particle in thermal conduction

Résumé

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 includinga 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.
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Dates et versions

hal-02502249 , version 1 (02-03-2022)

Identifiants

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Jean-François Barthélémy, François Bignonnet. The Eshelby problem of the confocal N-layer spheroid with imperfect interfaces and the notion of equivalent particle in thermal conduction. International Journal of Engineering Science, 2020, 150, pp.103274. ⟨10.1016/j.ijengsci.2020.103274⟩. ⟨hal-02502249⟩
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