On characterizing the set of possible effective tensors of composites: The variational method and the translation method. (English) Zbl 0751.73041

Milton, Graeme W.

Commun. Pure Appl. Math. 43, No. 1, 63-125 (1990).

This comprehensive paper is a sort of synthesis of various aspects of bounding techniques for conduction in composites and the elastic properties of composites. Bounds for dynamic problems in the quasi-static limit are also investigated, thus including the viscoelastic behaviour. Particularly, much attention is devoted to the Hashin-Shtrikman bounds and the translation method of Tartar and Murat and Lurie and Cherkaev. Relations between different techniques are carefully discussed. The dual approach is often exploited in finding bounds. Having formulated the polarization problem, it is shown that for layered materials this problem can be easily solved. The paper is written in a rather abstract way and will certainly appeal to mathematically minded researchers working on the mechanics of composites.

Reviewer: J.J.Telega (Warszawa)

MSC:

74E30	Composite and mixture properties
74S30	Other numerical methods in solid mechanics (MSC2010)
74P10	Optimization of other properties in solid mechanics
74E05	Inhomogeneity in solid mechanics

Keywords:

elementary bounds; conduction in composites; elastic properties of composites; quasi-static limit; Hashin-Shtrikman bounds; polarization problem; layered materials

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