Relaxed micromorphic modeling of the interface between a homogeneous solid and a band-gap metamaterial: New perspectives towards metastructural design

Angela Madeo (1, 2) , Gabriele Barbagallo (3) , Manuel Collet (4) , Marco Valerio D’agostino (1) , M. Miniaci (5) , Patrizio Neff (6)

1 M2S - Mécanique des Matériaux et des Structures
2 IUF - Institut universitaire de France
3 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
4 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
5 LOMC - Laboratoire Ondes et Milieux Complexes
6 Universität Duisburg-Essen = University of Duisburg-Essen [Essen]

In the present paper, the material parameters of the isotropic relaxed micromorphic model derived for a specific metamaterial in a previous contribution are used to model its transmission properties. Specifically, the reflection and transmission coefficients at an interface between a homogeneous solid and the chosen metamaterial are analyzed by using both the relaxed micromorphic model and a direct FEM implementation of the detailed microstructure. The obtained results show an excellent agreement between the transmission spectra derived via our enriched continuum model and those issued by the direct FEM simulation. Such excellent agreement validates the indirect measure of the material parameters and opens the way towards an efficient meta-structural design.

Mots clés: free micro-inertia; gradient micro-inertia; complete band-gaps; non-local; meta-structures; effects; relaxed micromorphic model; generalized continuum models; transmission; reflection

Domaines: Mécanique des solides [physics.class-ph]

Angela Madeo, Gabriele Barbagallo, Manuel Collet, Marco Valerio D’agostino, M. Miniaci, et al.. Relaxed micromorphic modeling of the interface between a homogeneous solid and a band-gap metamaterial: New perspectives towards metastructural design. Mathematics and Mechanics of Solids, 2018, 23 (12), pp.1485-1506. ⟨10.1177/1081286517728423⟩. ⟨hal-01720689⟩