Through the analysis of wave propagation, this paper presents the atypical dynamics of reticulated materials made of periodic frame structures (interconnected horizontal and vertical beams or plates). Emphasis is put on the non local effects in time and space and the fact that such materials can behave as second gradient media or meta-materials. Assuming the frame size is small compared to the wavelength, the homogenization method of periodic discrete media is applied to obtain the macroscopic behavior at the leading order. The mechanical features which characterize reticulated structures are introduced thanks to a systematic use of scaling. Moreover the method is adapted to situations with local resonance.
