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Exact estimates of the conductivity of a binary mixture of isotropic materials. (English) Zbl 0623.73011

Consider a mixture of two isotropic conducting mixtures of concentration \(m_ 1\) and \(m_ 2\), taking \(m_ 1+m_ 2=1\) and \(0\leq m_ i\leq 1\); and the conductivities as \(u_ 1\) and \(u_ 2\). The materials have an arbitrary microstructure including alignments. The main result proved is that the effective conductivity tensor forms a closed set. The Voigt- Reuss bounds are generalized for various possible microstructures in the form of upper and lower bounds. Special cases of layering and networking are considered as limiting cases and possible extensions when the materials are anisotropic are indicated.
Reviewer: E.S.R.Gopal

MSC:

74A40 Random materials and composite materials
82C70 Transport processes in time-dependent statistical mechanics
74A60 Micromechanical theories
74M25 Micromechanics of solids

Citations:

Zbl 0564.73079
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References:

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