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On the integral representation formula for a two-component elastic composite

✍ Scribed by Miao-Jung Ou; Elena Cherkaev

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 111 KB
Volume: 29
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.703

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✦ Synopsis

The aim of this paper is to derive, in the Hilbert space setting, an integral representation formula for the e ective elasticity tensor for a two-component composite of elastic materials, not necessarily wellordered. This integral representation formula implies a relation which links the e ective 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 e ective 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.

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