  In this note we show that the relaxed linear micromorphic model recently
proposed by the authors can be suitably used to describe the presence of
band-gaps in metamaterials with microstructures in which strong contrasts of
the mechanical properties are present (e.g. phononic crystals and lattice
structures). This relaxed micromorphic model only has 6 constitutive parameters
instead of 18 parameters needed in Mindlin- and Eringen-type classical
micromorphic models. We show that the onset of band-gaps is related to a unique
constitutive parameter, the Cosserat couple modulus $\mu_{c}$ which starts to
account for band-gaps when reaching a suitable threshold value. The limited
number of parameters of our model, as well as the specific effect of some of
them on wave propagation can be seen as an important step towards indirect
measurement campaigns.
