Kohn, Robert V.; Milton, Graeme W. 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 Cited in 1 ReviewCited in 19 Documents 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 PDF BibTeX XML