Asymptotic analysis of effective conductivity of composite materials with large rhombic fibers

The effective heat conductivity of composite materials formed by a regular array of large rhombic fibers embedded in a matrix is studied. Analytical solution is obtained by means of asymptotic homogenization method and with some further asymptotic approximations. The obtained results are equally applicable to determining different effective transport coefficients, such as dielectric constants, magnetic permeability, electric conductivity, etc. As the examples of the considered composite materials three possible limiting forms of two-component inhomogeneous structures with contacting inclusions are investigated. Obtained asymptotic results are discussed in relations to the known Dykhne formula.