On bounding the effective conductivity of anisotropic composites. (English) Zbl 0631.73012

Kohn, Robert V.; Milton, Graeme W.

Homogenization and effective moduli of materials and media, Proc. Workshop, Minneapolis/Minn. 1984/85, IMA Vol. Math. Appl. 1, 97-125 (1986).

[For the entire collection see Zbl 0622.00024.]
This inspiring paper examines three approaches to proving optimal bounds for anisotropic composites made by mixing two isotropic conducting materials in specified proportions. These bounds are achieved via: the compensated compactness method, the representation formulas and the Hashin-Shtrikman variational principles. Each of these methods is lucidly presented, including their comparison.

Reviewer: J.J.Telega

MSC:

74E05	Inhomogeneity in solid mechanics
74E10	Anisotropy in solid mechanics
74S30	Other numerical methods in solid mechanics (MSC2010)
74E30	Composite and mixture properties

Keywords:

optimal bounds; anisotropic composites; mixing two isotropic conducting materials; compensated compactness method; representation formulas; Hashin-Shtrikman variational principles