Aspects of Heterogenization

In this paper, we briefly review some of the recent developments in the methodology of heterogenization. A connection between a group structure on the set (−1, 1) of real numbers t such that −1 < t < 1, and the elastostatics of a multilayered fiber perfectly bonded to an infinite matrix is pointed out. Also, universal formulae, pertaining to the solution of two circular elastic inclusions perfectly bonded to a matrix, of infinite extent, which is subjected to arbitrary loading, are discussed. As a novel illustration of the heterogenization procedure, we study here the case where the inclusions are elastically (i.e., “imperfectly”) embedded in the matrix. Several cases are presented and discussed.