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