Asymptotic models for transport properties of densely packed, high-contrast fibre composites. Part II: Square lattices of rhombic inclusions and hexagonal lattices of circular inclusions. (15th November 2017) - Andrianov, Igor V.; Awrejcewicz, Jan; Starushenko, Galina A.
Abstract: This paper is a continuation of the investigations reported in the Part I. Based on the asymptotic approach and the lubrication theory, the composite with rhombic inclusions are studied. Models of composites with curvilinear rhombic inclusions and thin interfaces on phase boundaries are constructed with the help of non-smooth argument substitution and asymptotically equivalent functions. The effective conductivity is derived for absolutely conducting and non-conducting rhombic inclusions, taking into account thin interface effects. Generalisation of the classical Dykhne formula is proposed. Finally, asymptotic solutions are obtained for the effective conductivity of a hexagonal lattice with circular large-size and absolutely conducting/non-conducting inclusions.