title: First evidence of non-locality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model.
abstract: In this paper, we propose the first estimate of some elastic parameters of the relaxed micromorphic model on the basis of real experiments of transmission of longitudinal plane waves across an interface separating a classical Cauchy material (steel plate) and a phononic crystal (steel plate with fluid-filled holes). A procedure is set up in order to identify the parameters of the relaxed micromorphic model by superimposing the experimentally based profile of the reflection coefficient (plotted as function of the wave-frequency) with the analogous profile obtained via numerical simulations. We determine five out of six constitutive parameters which are featured by the relaxed micromorphic model in the isotropic case, plus the determination of the micro-inertia parameter. The sixth elastic parameter, namely the Cosserat couple modulusμc, still remains undetermined, since experiments on transverse incident waves are not yet available. A fundamental result of this paper is the estimate of the non-locality intrinsically associated with the underlying microstructure of the metamaterial. We show that the characteristic lengthLcmeasuring the non-locality of the phononic crystal is of the order of [Formula: see text] of the diameter of its fluid-filled holes.
authors.affiliation: LGCIE , Universitité de Lyon , 20 av. Albert Einstein, 69621, Villeurbanne cedex, France.
authors.forename: Angela
authors.identifier: 0000-0003-1940-9853
authors.initials: A
authors.lastname: Madeo
authors.affiliation: LGCIE, Universitité de Lyon, 20 av. Albert Einstein, 69621, Villeurbanne cedex, France; LaMCoS-CNRS, INSA-Lyon, Universitité de Lyon, 20 av. Albert Einstein, 69621, Villeurbanne cedex, France.
authors.forename: Gabriele
authors.initials: G
authors.lastname: Barbagallo
authors.affiliation: LGCIE , Universitité de Lyon , 20 av. Albert Einstein, 69621, Villeurbanne cedex, France.
authors.forename: Marco Valerio
authors.initials: MV
authors.lastname: d'Agostino
authors.affiliation: Università Telematica Internazionale UNINETTUNO , Corso Vittorio Emanuele II, 39, 00186 Roma, Italy.
authors.forename: Luca
authors.initials: L
authors.lastname: Placidi
authors.affiliation: Fakultät für Mathematik , Universität Duisburg-Essen , Thea-Leymann-Straße 9, 45127 Essen, Germany.
authors.forename: Patrizio
authors.initials: P
authors.lastname: Neff
keywords: complete band-gaps; generalized continuum models; multi-scale modelling; non-local effects; relaxed micromorphic model