First evidence of non-locality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model
| Autor: | Patrizio Neff, Marco Valerio d'Agostino, Angela Madeo, Gabriele Barbagallo, Luca Placidi |
|---|---|
| Přispěvatelé: | Laboratoire de Génie Civil et d'Ingénierie Environnementale (LGCIE), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Università telematica internazionale Uninettuno [Roma], Universität Duisburg-Essen [Essen] |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Characteristic length
AMS 2010: 74A10 74A30 74A60 74E15 74M25 74Q15 General Mathematics complete band-gaps General Physics and Astronomy FOS: Physical sciences 02 engineering and technology multi-scale modeling [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph] 01 natural sciences 0203 mechanical engineering non-local effects 0101 mathematics Reflection coefficient Research Articles Physics Condensed Matter - Materials Science Basis (linear algebra) Mathematical analysis Isotropy General Engineering Cauchy distribution Metamaterial Materials Science (cond-mat.mtrl-sci) generalized continuum models Function (mathematics) 74A10 74A30 74A60 74E15 74M25 74Q15 010101 applied mathematics Transverse plane 020303 mechanical engineering & transports relaxed micromorphic model Mathematik |
| Zdroj: | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2016, 472 (2190), ⟨10.1098/rspa.2016.0169⟩ |
| ISSN: | 1364-5021 1471-2946 |
| DOI: | 10.1098/rspa.2016.0169⟩ |
| Popis: | 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 of13of the diameter of its fluid-filled holes. |
| Databáze: | OpenAIRE |
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