Some theoretical, numerical and technical aspects of the homogenization theory

Abstract: This thesis in applied mathematics is devoted to some theoretical, numerical and technical aspects of the homogenization theory, and has obviously been deeply influented by interactions between mathematicians with knowledge in homogenization theory, scientists in composite engineering and the industry. It contains a number of theoretical, numerical and technical aspects of the homogenization theory and its applications. The thesis consists of five papers. In the first paper we give an elementary presentation of some basic ideas in the homogenization theory, which can serve as an introduction and frame to the author´s contributions to the papers in this thesis. The second paper presents some theory and numerical results concerning the effective elastic moduli of heterogeneous structures. In the third paper we consider in-plane stiffness properties of square symmetric unidirectional two-phase composites with given volume fractions. The fourth paper is concerned with the heat conduction in checkerboard structures.In particular, we present a new numerical method for determining the corresponding field which converges in the energy norm independent of the local conductivities. In the last paper we consider computational aspects of multiscale iterated honeycombs.