Three-phase model for a composite material with cylindrical circular inclusions. Part II: Application of Padé approximants

The solution of the Three-phase composite model (coinciding with the Maxwell Garnett formula) is transformed using the Padé approximants. The obtained Padé approximants fundamentally expand the applicability limits of the Maxwell Garnett solution. The explicit analytical formulae for the effective coefficient of thermal conductivity of the composite materials with periodic cylindrical inclusions of a circular cross-section are derived. The developed Padé approximants provide the accurate quantitative results as well as a qualitative picture of the asymptotic behavior for the effective coefficient of thermal conductivity for composites with inclusion of any conductivity, including the limiting cases of non-conducting and absolutely conducting inclusions; and with inclusions of small and large sizes, including very large, close to the limiting sizes.