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In this paper we study the reflective properties of a 2D interface separatinga homogeneous solid from a band-gap metamaterial by modeling it as an interfacebetween a classical Cauchy continuum and a relaxed micromorphic medium. We showthat the proposed model is able to predict the onset of Stoneley interfacewaves at the considered interface both at low and high-frequency regimes. Moreprecisely, critical angles for the incident wave can be identified, beyondwhich classical Stoneley waves, as well as microstructure-related Stoneleywaves appear. We show that this onset of Stoneley waves, both at low and highfrequencies, strongly depends on the relative mechanical properties of the twomedia. We suggest that a suitable tailoring of the relative stiffnesses of thetwo media can be used to conceive 'smart interfaces' giving rise to widefrequency bounds where total reflection or total transmission may occur.

Low-and high-frequency Stoneley waves, reflection and transmission at a Cauchy/relaxed micromorphic interface