Asymptotic models and transport properties of densely packed, high-contrast fibre composites. Part I: Square lattice of circular inclusions

Abstract

Homogenisation theory and lubrication approach are adopted to study transport problems for systems of densely packed, high-contrast fibre composites. The effective conductivity properties of composites with inclusions of various shapes are derived. Contact conditions are analysed for boundaries between the composite phases. In addition, asymptotic properties are investigated. The following problems are studied: composites with inclusions of large circular size and conductivity, located in a square lattice; composites with non-conducting inclusions, matrix-inclusions contact conditions as well as composites with thin interfaces at boundaries between different phases. Numerous results are obtained with the use of methods of the non-smooth argument substitution and asymptotically equivalent functions.