ABSTRACT
This chapter focuses on using asymptotically equivalent function for analysis of composite structures. It begins with determination of the effective thermal conductivity coeffcient by matching of asymptotic expansions. The latter thematic issue includes statement of the problem and constitutive relations, matching of asymptotic expansions in the case of high and low conductivity of inclusions, analysis of the effective thermal conductivity coefficient in limiting cases, and remarks on the effectiveness of the Hashin-Shtrikman bounds. The analysis covers problems of non-intersecting rhombic inclusions of large sizes, intersecting of rhombic inclusions, rhombic inclusions in contact, asymptotic expressions for the effective coefficient, composites with equally represented phases and Dykhne structure, and physical equivalence of chess composite arrays. Determining the effective characteristics of inhomogeneous media is one of the main problems in the mechanics of composites. The solution of the problem is based on the use of the homogenization method followed by the application of asymptotic representations.
