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Band gaps in the relaxed linear micromorphic continuum

Abstract : In this note we show that the relaxed linear micromorphic model recently proposed by the authors can be suitably used to describe the presence of band-gaps in metamaterials with microstructures in which strong contrasts of the mechanical properties are present (e.g. phononic crystals and lattice structures). This relaxed micromorphic model only has 6 constitutive parameters instead of 18 parameters needed in Mindlin- and Eringen-type classical micromorphic models. We show that the onset of band-gaps is related to a unique constitutive parameter, the Cosserat couple modulus (c) which starts to account for band-gaps when reaching a suitable threshold value. The limited number of parameters of our model, as well as the specific effect of some of them on wave propagation can be seen as an important step towards indirect measurement campaigns.
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Contributor : Thibault Lemaire Connect in order to contact the contributor
Submitted on : Thursday, November 13, 2014 - 1:20:04 PM
Last modification on : Wednesday, February 23, 2022 - 3:55:55 PM

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A. Madeo, P. Neff, Ionel-Dumitrel Ghiba, L. Placidi, Giuseppe Rosi. Band gaps in the relaxed linear micromorphic continuum. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley-VCH Verlag, 2014, 95 (9), pp.880-887. ⟨10.1002/zamm.201400036⟩. ⟨hal-01082378⟩



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