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 our model by superimposing the experimentally-based profile of the reflection coefficient (plotted as function of the frequency of the traveling waves) with the analogous profile obtained via simulations based upon the relaxed micromorphic model. We end up with the determination of 5 out of 6 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 modulus ${\mu }_c$, still remains undetermined, since experimental data concerning the transmission properties of the considered interface for transverse incident waves are not yet available. A fundamental result of the present paper is the estimate of the non-locality intrinsically associated to the underlying microstructure of the metamaterial. As a matter of fact, we appraise that the characteristic length $L_c$ measuring the non-locality of the considered phononic crystal is of the order of $1/3$ of the diameter of the considered fluid-filled holes.

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Cited by in corpus (6)

• Reflection and transmission of elastic waves at interfaces embedded in non-local band-gap metamaterials: a comprehensive study via the relaxed micromorphic model
• Real wave propagation in the isotropic relaxed micromorphic model
• Relaxed micromorphic model of transient wave propagation in anisotropic band-gap metastructures
• On the role of micro-inertia in enriched continuum mechanics
• Low-and high-frequency Stoneley waves, reflection and transmission at a Cauchy/relaxed micromorphic interface
• On the dispersion of waves for the linear thermoelastic relaxed micromorphic model