Abstract: Different homogenization schemes are discussed in viewof the order relations for the different length scales. The emphasis is thenplaced on the micro-macro transition from local micropolar mediums to ahomogenized Cauchy medium, suitable for the following order relation of thelength scales $L \gg l \gg A \approx l_m $. The microstructural size effectcan be naturally taken into account in the proposed homogenization scheme.This method is useful for the metal matrix composites, foam matrixcomposites and nanocomposites, in which the microstructural length scales ofthe matrix are important compared to that of the reinforced phase.