Unified complex variable solution for the effective transport properties of composites with a doubly-periodic array of fibers

We present a complex variable method to evaluate the transverse effective transport properties of composites with a doubly-periodic array of fibers. The obtained complex variable solution is derived in a unified form for arbitrary doubly-periodic fiber arrays and different fiber-matrix interfaces i.e. perfect interface contact resistance interface and coating. The present method can be seen as an extension of the method originated by Rayleigh only for symmetric fiber arrays. The limitation of Rayleigh's method is overcome by introducing a supplementary equation. Explicit formulae of the effective transport properties approximated to finite orders are obtained which are written in a regular form for different fiber arrays and reveal the reciprocal relations for symmetric fiber arrays. The validity and accuracy of the solution are verified by numerical examples and comparisons with existing methods. (c) 2016 WILEY-VCH Verlag GmbH & Co. KGaA Weinheim