Reflection and transmission of elastic waves at interfaces embedded in non-local band-gap metamaterials: a comprehensive study via the relaxed micromorphic model

Abstract

In this paper we derive, by means of a suitable least action principle, the duality jump conditions to be imposed at surfaces of discontinuity of the material properties in non-dissipative, linear-elastic, isotropic, Mindlin's and relaxed micromorphic media, respectively. The introduced theoretical framework allows the transparent set-up of different types of micro-macro connections which are intrinsically compatible with the governing bulk equations. To illustrate the interest of the many introduced jump conditions, we focus on the case of an interface between a classical Cauchy continuum on one side and a relaxed micromorphic one on the other side. As expected, we find a complete reflection in the frequency intervals for which band-gaps are known to occur in the relaxed micromorphic continuum and precise microstructure-related reflective patterns are identified. We repeat a similar study for analogous connections between a classical Cauchy continuum and a Mindlin's micromorphic one and we show that the reflective properties of the considered interfaces are drastically modified due to the fact that band-gaps are not allowed in standard Mindlin's micromorphic media. The present work opens the way towards the possibility of conceiving complex metastructures in which band-gap metamaterials and classical materials are coupled together to produce structures with completely new and unorthodox properties with respect to wave propagation, transmission and reflection. Last, but not least, indirect measurements of the material coefficients of the relaxed micromorphic model based upon real experiments of reflection and transmission in band-gap metamaterials are uncovered by the present work which makes them finally realizable in the short term.

References in corpus (3)

• Photonic band gap in isotropic hyperuniform disordered solids with low dielectric contrast
• Wave propagation in relaxed micromorphic continua: modelling metamaterials with frequency band-gaps
• First evidence of non-locality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model

Cited by in corpus (14)

• First evidence of non-locality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model
• Real wave propagation in the isotropic relaxed micromorphic model
• Size-effects of metamaterial beams subjected to pure bending: on boundary conditions and parameter identification in the 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
• Nečas-Lions lemma revisited: An $L^p$-version of the generalized Korn inequality for incompatible tensor fields
• Primal and mixed finite element formulations for the relaxed micromorphic model
• Lagrange and $H(\mathrm{curl},\mathcal{B})$ based Finite Element formulations for the relaxed micromorphic model
• A computational approach to identify the material parameters of the relaxed micromorphic model
• 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
• A global higher regularity result for the static relaxed micromorphic model on smooth domains
• A note on local higher regularity in the dynamic linear relaxed micromorphic model
• A hybrid H1xH(curl) finite element formulation for a relaxed micromorphic continuum model of antiplane shear