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On the integral representation formula for a two‐component elastic composite
Author(s) -
Ou MiaoJung,
Cherkaev Elena
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.703
Subject(s) - homogenization (climate) , mathematics , viscoelasticity , composite number , elasticity (physics) , elastic modulus , moduli , mathematical analysis , inverse , linear elasticity , hilbert space , representation (politics) , composite material , geometry , finite element method , materials science , algorithm , physics , politics , political science , law , thermodynamics , biodiversity , ecology , quantum mechanics , biology
The aim of this paper is to derive, in the Hilbert space setting, an integral representation formula for the effective elasticity tensor for a two‐component composite of elastic materials, not necessarily well‐ordered. This integral representation formula implies a relation which links the effective elastic moduli to the N ‐point correlation functions of the microstructure. Such relation not only facilitates a powerful scheme for systematic incorporation of microstructural information into bounds on the effective elastic moduli but also provides a theoretical foundation for inverse‐homogenization. The analysis presented in this paper can be generalized to an n ‐component composite of elastic materials. The relations developed here can be applied to the inverse‐homogenization for a special class of linear viscoelastic composites. The results will be presented in another paper. Copyright © 2005 John Wiley & Sons, Ltd.
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