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The dispersion tensor and its unique minimizer in Hashin-Shtrikman micro-structures. (English) Zbl 1398.35230

Summary: 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 [L. Tartar, The general theory of homogenization. A personalized introduction. Berlin: Springer (2009; Zbl 1188.35004)]. 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.

MSC:

35Q74 PDEs in connection with mechanics of deformable solids
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
74Q20 Bounds on effective properties in solid mechanics
49K20 Optimality conditions for problems involving partial differential equations
74A60 Micromechanical theories
35P15 Estimates of eigenvalues in context of PDEs
74M25 Micromechanics of solids
74A40 Random materials and composite materials

Citations:

Zbl 1188.35004
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References:

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