  Exploring the dynamical response of mechanical metamaterials has gathered
increasing attention in the last decades, enabling the design of
microstructures exotically interacting with elastic waves (focusing,
channeling, band-gaps, negative refraction, cloaking, and many more). Yet, the
application and use of such metamaterials in engineering practice is still
deficient due to the lack of effective models unveiling metamaterials'
interactions with more classical materials at finite scales. In this paper, we
show that the relaxed micromorphic model can bring an answer to this open
problem and can be effectively used to explore and optimize metamaterials'
structures consisting of metamaterials' and classical materials' bricks of
finite size. We investigate two examples, namely a double-shield structure that
can be used to widen the frequency range for which the internal region can be
protected and a multiple-shield structure that optimizes both the screening of
the regions internal to the single shields and of the zones exterior to the
shields themselves. The exploration of these complex meta-structures has been
enabled by the finite element implementation of the relaxed micromorphic model
that predicts their response at a fraction of the computational cost when
compared to classical simulations.
