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Modelling effective properties of composite materials using the inclusion concept. General considerations

Vieville P., Bonnet A. S., Lipiński P.

Archives of Mechanics

2006

Vol. 58, nr 3

207-239

This paper is devoted to some general theoretical considerations concerning the modelling of the effective properties of composite materials based on the inclusion concept. Starting from the kinematical integral equation for inhomogeneous materials, all principal homogenisation methods are reviewed and analysed. Special attention is focused on three approaches, namely the self-consistent scheme, the Mori-Tanaka method and incremental procedure derived from the differential scheme. Mono-site and multi-site versions of these approximate solutions are considered. Limitations of the traditional self-consistent scheme are recognized. Improvements are proposed such as composite or coated inclusions and the incremental method mentioned above. Direct and iterative procedures allowing the determination of strain concentration tensors derived from the integral equation are established. The numerical implementation of all the schemes presented in this article will be considered in the next paper. Extreme configurations will be analysed such as composites with voids or very stiff inclusions with respect to matrix properties.