The microscopic conduction fields in the multi-coated sphere composites under the imposed macroscopic gradient and flux fields

  • Duc Chinh PhamEmail author
  • Trung Kien Nguyen


Explicit analytical expressions of the microscopic conduction (gradient or flux) fields in the d-dimensional (\(d=2,3\)) multi-coated sphere assemblages under the imposed macroscopic gradient and flux fields are presented. Limiting procedures are developed to derive the results for most important specific composites, which include the inclusion composites with highly conducting imperfect interface, lowly conducting (with Kapitza resistance) imperfect interface, general imperfect interface, and those with anisotropic coatings. When the volume proportion of the outermost shells of the assemblages approaches 1, the simplified results for the dilute suspensions of the complex spherically symmetric inclusions in a major matrix are deduced.


Conduction (gradient or flux) fields Multi-coated sphere assemblage Imperfect interfaces Anisotropic coating 

Mathematics Subject Classification

74E30 74Q05 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.VAST - Institute of MechanicsHanoiVietnam
  2. 2.Division of Structures, Department of Civil Engineering, Research and Application Center for Technology in Civil EngineeringUniversity of Transport and CommunicationsHanoiVietnam

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