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Optimal bounds for conduction in two-dimensional, two-phase, anisotropic media. (English) Zbl 0668.73018

Non-classical continuum mechanics, Proc. Symp., Durham/Engl. 1985, Lond. Math. Soc. Lect. Note Ser. 122, 197-212 (1987).
[For the entire collection see Zbl 0657.00013.]
The paper is concerned with the determination of the set of all possible effective conductivities of a two-phase anisotropic material. A family of conductivity tensors with respect to a mixture of the two phases is defined, its macroscopic behaviour is investigated with the aid of H- convergence theory. The complete characterization of all effective tensors regarding the two phase-associated ones is shown to depend on the relative magnitudes of their eigenvalues.
Reviewer: H.-J.Mieth

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74E10 Anisotropy in solid mechanics
74A15 Thermodynamics in solid mechanics

Citations:

Zbl 0657.00013