Title

On The Representation Formula For Well-Ordered Elastic Composites: A Convergence Of Measure Approach

Keywords

Helly's theorems; Integral representation formula; Microstructure; Positive Borel measure; Well-ordered composites

Abstract

The aim of this paper is to derive an integral representation formula for the effective elasticity tensor for a two-component well-ordered composite of elastic materials without using a third reference medium and without assuming the completeness of the eigenspace of the operator G defined in (2.16) in (J. Mech. Phys. Solids 1984; 32(1):41-62). As shown in (J. Mech. Phys. Solids 1984; 32(1):41-62) and (Math. Meth. Appl. Sci. 2006; 29(6):655-664), 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 de-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 de-homogenization for a special class of linear viscoelastic composites. The results will be presented in another paper. Copyright © 2006 John Wiley & Sons, Ltd.

Publication Date

5-10-2007

Publication Title

Mathematical Methods in the Applied Sciences

Volume

30

Issue

7

Number of Pages

851-860

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1002/mma.818

Socpus ID

34247338058 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/34247338058

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