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Effective conductivity of spheroidal particle composite with imperfect interfaces: Complete solutions for periodic and random micro structures
Affiliation:1. Institute for Superhard Materials of the National Academy of Sciences, 04074 Kiev, Ukraine;2. Department of Mechanical Engineering, New Mexico State University, PO Box 30001, Las Cruces, NM 88003, USA;1. LPHE, Modeling & Simulations, Faculty of Science, Mohammed V University, Rabat, Morocco;2. CPM, Center of Physics and Mathematics, Faculty of Science, Mohammed V University, Rabat, Morocco;1. G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 801 Ferst Drive NW, Atlanta, GA 30332, USA;2. Pacific Northwest National Laboratory, 902 Battelle Blvd, Richland, WA 99352, USA;3. School of Materials Science and Engineering, Georgia Institute of Technology, 771 Ferst Drive NW, Atlanta, GA 30332, USA;1. Service de Metrologie Nucleaire, Universite Libre de Bruxelles (CP165/84), Avenue F.D.Roosevelt, 50 1050 Bruxelles, Belgium;2. Institute of Radiological Protection and Nuclear Safety, PRP-DGE/SRTG/LETIS, BP 17, 92262 Fontenay-aux-Roses, France;3. Bel V Rue Walcourt 148, 1070 Anderlecht, Belgium;4. Department of Chemistry, University of Helsinki, P.O. Box 55, 00014 Helsinki, Finland;1. Université de Lyon, INSA-Lyon, MATEIS CNRS UMR5510, 7 Avenue Jean Capelle, F-69621 Villeurbanne, France;2. Arts et Métiers ParisTech, LEM3 – UMR CNRS 7239, Ile du Saulcy, F-57045 Metz cedex 01, France
Abstract:The rigorous analytical approach to the conductivity homogenization problem for spheroidal particle composite with imperfect interfaces has been developed. The complete multipole series solution for a single inclusion with imperfect interface constitutes mathematical background of the work and provides a basic building block for the Maxwell and Rayleigh homogenization schemes. The low- and highly conducting spheroidal interface are considered in a unified way. The developed theory enables an analysis of composites of periodic and random micro structure with imperfect interfaces. Numerical study shows quite a significant combined effect of micro structure and imperfect interfaces on the macroscopic conductivity of composite. The obtained accurate solution serves as a benchmark for the known approximate theories. Their error due to neglecting the interaction effects and simplified treating the imperfect interfaces is estimated.
Keywords:Composite  Spheroid  Imperfect interface  Multipole expansion  Effective conductivity
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