  The conception of new metamaterials showing unorthodox behaviors with respect
to elastic wavepropagation has become possible in recent years thanks to
powerful dynamical homogenization techniques. Such methods effectively allow to
describe the behavior of an infinite medium generated by periodically
architectured base materials. Nevertheless, when it comes to the study of the
scattering properties of finite-sized structures, dealing with the correct
boundary conditions at the macroscopicscale becomes challenging. In this paper,
we show how finite-domain boundary value problems canbe set-up in the framework
of enriched continuum mechanics (relaxed micromorphic model) by imposing
continuity of macroscopic displacement and of generalized traction when
non-local effects areneglected.The case of a metamaterial slab of finite width
is presented, its scattering properties are studied viaa semi-analytical
solution of the relaxed micromorphic model and compared to numerical
simulationsencoding all details of the selected microstructure. The reflection
coefficient obtained via the twomethods is presented as a function of the
frequency and of the direction of propagation of the incidentwave. We find
excellent agreement for a large range of frequencies going from the long-wave
limitto frequencies beyond the first band-gap and for angles of incidence
ranging from normal to nearparallel incidence. The case of a semi-infinite
metamaterial is also presented and is seen to be areliable measure of the
average behavior of the finite metastructure. A tremendous gain in termsof
computational time is obtained when using the relaxed micromorphic model for
the study of theconsidered metastructure.
