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Archive for Rational Mechanics and Analysis

, Volume 230, Issue 2, pp 665–700 | Cite as

The Dispersion Tensor and Its Unique Minimizer in Hashin–Shtrikman Micro-structures

  • Loredana Bălilescu
  • Carlos Conca
  • Tuhin Ghosh
  • Jorge San Martín
  • Muthusamy Vanninathan
Article

Abstract

In this paper, we introduce a macroscopic quantity, namely the dispersion tensor or the Burnett coefficients in the class of generalized Hashin–Shtrikman micro-structures (Tartar in The general theory of homogenization, volume 7 of Lecture notes of the Unione Matematica Italiana, Springer, Berlin, p 281, 2009). In the case of two-phase materials associated with the periodic Hashin–Shtrikman structures, we settle the issue that the dispersion tensor has a unique minimizer, which is the so called Apollonian–Hashin–Shtrikman micro-structure.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Loredana Bălilescu
    • 1
    • 2
  • Carlos Conca
    • 3
  • Tuhin Ghosh
    • 4
  • Jorge San Martín
    • 3
  • Muthusamy Vanninathan
    • 5
  1. 1.Department of Mathematics and Computer ScienceUniversity of PiteştiPiteştiRomania
  2. 2.Department of MathematicsFederal University of Santa CatarinaFlorianópolisBrazil
  3. 3.Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático UMR 2071/UMI 2807 CNRS-UChile, and Centro de Biotecnología y BioingenieríaFacultad de Ciencias Físicas y Matemáticas, Universidad de ChileSantiagoChile
  4. 4.Centre For Applicable MathematicsTata Institute of Fundamental ResearchBangaloreIndia
  5. 5.Department of MathematicsIIT-BombayMumbaiIndia

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