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In this paper the relaxed micromorphic material model for anisotropicelasticity is used to describe the dynamical behavior of a band-gapmetamaterial with tetragonal symmetry. Unlike other continuum models (Cauchy,Cosserat, second gradient, classical Mindlin-Eringen micromorphic etc.), therelaxed micromorphic model is endowed to capture the main microscopic andmacroscopic characteristics of the targeted metamaterial, namely, stiffness,anisotropy, dispersion and band-gaps. The simple structure of our materialmodel, which simultaneously lives on a micro-, a meso- and a macroscopic scale,requires only the identification of a limited number of frequency-independentand thus truly constitutive parameters, valid for both static andwave-propagation analyses in the plane. The static macro- and micro- parametersare identified by numerical homogenization in static tests on the unit-celllevel in [30]. The remaining inertia parameters for dynamical analyses arecalibrated on the dispersion curves of the same metamaterial as obtained by aclassical Bloch-Floquet analysis for two wave directions. We demonstrate viapolar plots that the obtained material parameters describe very well theresponse of the structural material for all wave directions in the plane, thuscovering the complete panorama of anisotropy of the targeted metamaterial.

Effective description of anisotropic wave dispersion in mechanical band-gap metamaterials via the relaxed micromorphic model