![]() In this thesis, the finite element method is used to perform transient analysis of wavepacket propagation in different mediums. The concept of the presence of interfaces has been largely exploited for efficiently manipulating phonons from long-wavelength to nanometric wavelengths, i.e., frequencies in THz regime, responsible for thermal transport at room temperature. Heat transfer is actually intimately related to the sound propagation (acoustic transfer) in materials, as in insulators and semi-conductors the main heat carriers are acoustic phonons. 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 $^2$ dependency, including the influence of 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. 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. Crucially, a correct description needs to describe both the extrinsic interface-induced and the intrinsic atomic scale-originated phonon scattering. 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. Structured metamaterials are at the core of extensive research, promising for thermal and acoustic engineering. In this work, we propose a continuum viscoelastic model based on the hierarchical strategy multi-scale approach, able to reproduce well the phonon attenuation in a large frequency range, spanning three orders of magnitude from GHz to THz with a ω2−ω4−ω2 dependence, including the influence of temperature. Crucially, a correct description needs to describe both the extrinsic interface-induced and the intrinsic atomic scale-originated phonon scattering, especially when the component material is made of glass, a highly dissipative material in which wave attenuation is strongly dependent on frequency as well as on temperature. Nevertheless, the computational cost required for correctly simulating large systems imposes to use a continuous model to describe the effective behavior without knowing the atomistic details. Structured metamaterials are at the core of extensive research, promising for acoustic and thermal engineering.
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