On the representation formula for well-ordered elastic composites: A convergence of measure approach

    Authors

    M. J. Ou

    Comments

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    Abbreviated Journal Title

    Math. Meth. Appl. Sci.

    Keywords

    integral representation formula; well-ordered composites; microstructure; positive Borel measure; Helly's theorems; BOUNDS; Mathematics, Applied

    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) over cap 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 (c) 2006 John Wiley & Sons, Ltd.

    Journal Title

    Mathematical Methods in the Applied Sciences

    Volume

    30

    Issue/Number

    7

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    851

    Last Page

    860

    WOS Identifier

    WOS:000245858000005

    ISSN

    0170-4214

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