Boundary and interface conditions in the relaxed micromorphic model : Exploring finite-size metastructures for elastic wave control

ORCID
0000-0002-5967-5403
Affiliation
Faculty of Architecture and Civil Engineering, TU Dortmund, Dortmund, Germany
Rizzi, Gianluca;
Affiliation
GEOMAS, INSA-Lyon, Université de Lyon, Villeurbanne Cedex, France
d’Agostino, Marco Valerio;
GND
122258886
ORCID
0000-0002-1615-8879
LSF
13332
Affiliation
Fakultät für Mathematik, Universität Duisburg-Essen, Essen, Germany
Neff, Patrizio;
Affiliation
Faculty of Architecture and Civil Engineering, TU Dortmund, Dortmund, Germany
Madeo, Angela

In this paper, we establish well-posed boundary and interface conditions for the relaxed micromorphic model that are able to unveil the scattering response of fully finite-size metamaterial samples. The resulting relaxed micromorphic boundary value problem is implemented in finite-element simulations describing the scattering of a square metamaterial sample whose side counts nine unit cells. The results are validated against a direct finite-element simulation encoding all the details of the underlying metamaterial’s microstructure. The relaxed micromorphic model can recover the scattering metamaterial’s behavior for a wide range of frequencies and for all possible angles of incidence, thus showing that it is suitable to describe dynamic anisotropy. Finally, thanks to the model’s computational performances, we can design a metastructure combining metamaterials and classical materials in such a way that it acts as a protection device while providing energy focusing in specific collection points. These results open important perspectives for the short-term design of sustainable structures that can control elastic waves and recover energy.

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