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

摘要

In this paper we derive, by means of a suitable least action principle, theduality jump conditions to be imposed at surfaces of discontinuity of thematerial properties in non-dissipative, linear-elastic, isotropic, Mindlin'sand relaxed micromorphic media, respectively. The introduced theoreticalframework allows the transparent set-up of different types of micro-macroconnections which are intrinsically compatible with the governing bulkequations. To illustrate the interest of the many introduced jump conditions,we focus on the case of an interface between a classical Cauchy continuum onone side and a relaxed micromorphic one on the other side. As expected, we finda complete reflection in the frequency intervals for which band-gaps are knownto occur in the relaxed micromorphic continuum and precisemicrostructure-related reflective patterns are identified. We repeat a similarstudy for analogous connections between a classical Cauchy continuum and aMindlin's micromorphic one and we show that the reflective properties of theconsidered interfaces are drastically modified due to the fact that band-gapsare not allowed in standard Mindlin's micromorphic media. The present workopens the way towards the possibility of conceiving complex metastructures inwhich band-gap metamaterials and classical materials are coupled together toproduce structures with completely new and unorthodox properties with respectto wave propagation, transmission and reflection. Last, but not least, indirectmeasurements of the material coefficients of the relaxed micromorphic modelbased upon real experiments of reflection and transmission in band-gapmetamaterials are uncovered by the present work which makes them finallyrealizable in the short term.