Homogenization of non-periodic zones in periodic domains using the embedded unit cell approach

In this paper we present the development of the embedded unit cell (EUC) approach, a new concept designed to facilitate homogenization and multi scale analysis of composite materials/domains in cases where the classical theory of homogenization is not valid due to lack of periodic microscopic response, e.g. in the boundary of a periodic macroscopic domain. The EUC approach is based on a non-periodic formulation of the asymptotic homogenization theory and evaluates the local/micro response of non-periodic zones, based on alternative boundary conditions. Finally, a verification study, which demonstrates the appropriate numerical performance of the suggested homogenization approach, is presented.