  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.
