Conduction in 2-D and 3-D dimensional spherically-symmetric anisotropic-coating inclusion composites

Based on the variational three-point correlation results for the conductivity (thermal, electrical,...) of the multi-coated sphere assemblages, limiting procedures have been developed to construct the explicit expressions of the macroscopic conductivity and the respective microscopic gradient and fl...

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Bibliographic Details
Published in:International journal of engineering science 2020-09, Vol.154, p.103352, Article 103352
Main Authors: Nguyen, Trung-Kien, Pham, Duc-Chinh, Nguyen, Van-Luat
Format: Article
Language:English
Subjects:
Anisotropic coating
Anisotropy
Coating
Composite materials
Conductivity
Effective conductivity
Electrical resistivity
Flux
Inclusions
Lower bounds
Microscopic conduction fields
Spherical shells
Spherically-symmetric inclusion composites
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Summary:Based on the variational three-point correlation results for the conductivity (thermal, electrical,...) of the multi-coated sphere assemblages, limiting procedures have been developed to construct the explicit expressions of the macroscopic conductivity and the respective microscopic gradient and flux fields for spherically-symmetric inclusion composites with anisotropic coating in d dimensions (d=2,3) under both the imposed macroscopic gradient or flux fields. Numerical examples are provided, verifying the convergence of the results for the macroscopic conductivity obtained from the minimum energy upper and lower bound approaches, and also that derived from the differential one. Explicit formal and numerical expressions of the microscopic conduction fields and illustration pictures of the microscopic flux lines within and around the typical anisotropic coating inclusion are also given. When the volume proportion of the outermost spherical shell increases to be the predominant one, one obtains the respective exact results for the important specific case of dilute solution of the anisotropic-coating inclusions suspended in the major matrix phase.
ISSN:0020-7225
1879-2197
DOI:10.1016/j.ijengsci.2020.103352