Numerous materials and structures of various sizes can be considered as periodic reticulated (or cellular) systems, that is to say they are obtained by repeating a unit cell made up of interconnected beams (or plates). As beams are much stiffer in tension-compression than in bending, the propagation of compressional waves with wavelengths much greater than the cell size and the bending modes of the elements can occur in the same frequency range. Thus reticulated materials can behave as metamaterials and exhibit unusual dynamic properties.The consequences of this phenomenon are investigated by considering the archetypal case of frame materials. Since the condition of scale separation is respected for the compressional waves, the homogenization method of periodic discrete media is used to rigorously derive the macroscopic behavior at the leading order. The results are also confirmed by numerical simulations.
