Effective conductivity of a composite material with non-ideal contact conditions

Abstract

The effective conductivity of 2D doubly periodic composite materials with circular disjoint inclusions under non-ideal contact conditions on the boundary between material components is found. The obtained explicit formula for the effective conductivity contains all parameters of the considered model, such as the conductivities of matrix and inclusions, resistance coefficients, radii and centres of the inclusions and also the values of special Eisenstein functions. The method of functional equations is used to analyse the conjugation problem for analytic functions which is equivalently derived from the initial problem. Existence and uniqueness for the solution of the problem is obtained by using a reduction to a certain mixed boundary value problem for analytic functions in special functional spaces.

Keywords:

• 2D composite material
• steady-state conductivity problem
• effective conductivity
• non-ideal contact conditions
• functional equations

AMS Subject Classifications::

• 30E25
• 35B27
• 74Q05

Acknowledgements

This work is partially supported by Unidade de Investigação Matemática e Aplicações of Universidade de Aveiro through the Portuguese Science Foundation (FCT–Fundação para a Ciência e a Tecnologia) and by the Belarusian Fund for Fundamental Scientific Research. E. Pesetskaya is supported by the Portuguese Science Foundation through grant number SFRH/BPD/34649/2007.