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Effective conductivity of composite materials with random positions of cylindrical inclusions: finite number inclusions in the cell

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The effective conductivity of composite materials with random position n 2 , n ∈ N , and the cylindrical identical inclusions inside periodic cells is considered. We compare the results for symmetric and nonsymmetric cases of location of the inclusions in the cells and find that a symmetric structure provides a minimum for the effective conductivity among all the structures having n 2 inclusions of such conductivity and sizes.

Keywords: 35B27; 74Q05; AMS Subject Classifications: 30E25; Boundary value problems; Clausius–Mossotti formula; Complex potential; Composite materials; Effective conductivity; Method of functional equations; Random inclusions

Document Type: Research Article


Affiliations: Communicated by R.P. Gilbert

Publication date: August 1, 2005

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