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Zbl 0631.73011
Milton, G.W.
Modelling the properties of composites by laminates. (English)
[A] Homogenization and effective moduli of materials and media, Proc. Workshop, Minneapolis/Minn. 1984/85, IMA Vol. Math. Appl. 1, 150-174 (1986).

[For the entire collection see Zbl 0622.00024.] \par This paper deals mainly with a modelling of the functional dependence of the effective conductivity by laminates. The author discusses the existing results and proposes many open problems. Analogies with electrical network problems are also examined, and approaches using G- closures and variational methods are briefly reviewed. \par To an exhaustive list of references I would like to add an excellent review paper by {\it K. A. Lur}'e and {\it A. V. Cherkaev}: Effective characteristics of composites and optimum structural design, Uspechi Mechaniki 9, 3-81 (Russian) (1986). \par In an appendix the author discusses the connection between transformations used by other writers to derive bounds on the effective dielectric constant (or conductivity) and the work by {\it G. A. Baker} [J. Math. Phys. 10, 814-820 (1969; Zbl 0175.361)]. \par The paper will surely be of interest to physically oriented researchers in the field of composite materials.
[J.J.Telega]

MSC 2000:: *74E05 Inhomogeneity
74E30 Composite and mixture properties
74F15 Electromagnetic effects
74S30 Other numerical methods

Keywords: Hashin-Shtrikman bounds; Stieltjes functions; functional dependence; effective conductivity; laminates; electrical network problems; G- closures; transformations; bounds on the effective dielectric constant

Citations: Zbl 0622.00024; Zbl 0175.361

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