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

Abstract

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:

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

Acknowledgments

The author is grateful to Vladimir Mityushev for drawing attention to the investigation of the properties of composite materials and for the helpful discussions for the further study of the conducting properties of composites.

The author is also grateful to Sergei Rogosin for his attention and assistance during this work on the article.

Notes

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Additional information

Notes on contributors

Ekaterina V. Pesetskaya *

Email: [email protected]