Modelling the properties of composites by laminates. (English) Zbl 0631.73011

Milton, G. W.

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.]
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.
To an exhaustive list of references I would like to add an excellent review paper by K. A. Lur’e and A. V. Cherkaev: Effective characteristics of composites and optimum structural design, Uspechi Mechaniki 9, 3-81 (Russian) (1986).
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 G. A. Baker [J. Math. Phys. 10, 814-820 (1969; Zbl 0175.361)].
The paper will surely be of interest to physically oriented researchers in the field of composite materials.

Reviewer: J.J.Telega

MSC:

74E05	Inhomogeneity in solid mechanics
74E30	Composite and mixture properties
74F15	Electromagnetic effects in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)

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