On the G-closure in the polycrystalline problem

V Nesi

Research output: Contribution to journalArticle

Abstract

This work is concerned with the G-closure problem for electrical conductivity in three space dimensions in the context of polycrystalline composites. Its specific goal is to explore the attainability of a certain lower bound. This bound was proved by Avellaneda et al. [J. Appl. Phys., 63 (1988), pp. 4989-5003]. In the case of uniaxial basic crystal and isotropic composites, the bound was conjectured by Schulgasser [J. Appl. Phys., 54 (1983), p. 1380]. The former work established the attainability of this bound only under very special circumstances, e.g., when the basic crystal is uniaxial. The main conclusion of the present work is that, in the general case, when the conductivity tensor of the basic crystal has distinct eigenvalues, the lower bound is always attained by a two-dimensional set of rank-one laminates.

Original languageEnglish
Pages (from-to)96-127
Number of pages32
JournalSIAM Journal on Applied Mathematics
Volume53
Issue number1
Publication statusPublished - Feb 1993

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