Structured metamaterials are at the core of extensive research, promising for thermal and acoustic engineering. However, the computational cost required for correctly simulating large systems imposes to use continuous modeling, able to grasp the physics at play without entering in the atomistic details. Crucially, a correct description needs to describe both the extrinsic interface-induced and the intrinsic atomic scale-originated phonon scattering. This latter becomes considerably important when the metamaterial is made out of a glass, which is intrinsically highly dissipative and with a wave attenuation strongly dependent on frequency and temperature. In amorphous systems, the effective acoustic attenuation triggered by multiple mechanisms is now well characterized and exhibits a nontrivial frequency dependence with a double crossover of power laws. Here we propose a continuum mechanical model for a viscoelastic medium, able to bridge atomic and macroscopic scales in amorphous materials and reproduce well the phonon attenuation from GHz to THz with a ${omega}^2-{omega}^4-{omega}^2$ dependency, including the influence of temperature.
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