Nanophononic materials have recently arisen as a promising way for controlling heat transport, mirroring the results in macroscopic phononic materials for sound transmission, filtering and attenuation applications. Here we present a Finite Element numerical simulation of the transient propagation of an acoustic Wave-Packet in a 2D nanophononic material, which allows to identify the effect of the nanostructuration on the acoustic attenuation length and thus on the transport regime for the vibrational energy. Assuming elastic behavior in the matrix and in the inclusions, we find that the rigidity contrast between them not only tunes the apparent attenuation length of the wave packet along its main trajectory, but gives rise to different behaviours, from weak to strong scattering, and waves pinning. As a consequence, different energy transport regimes can be identified in the three-parameter space of the excitation frequency, inclusions size and rigidity contrast, leading to the identification of a combination of parameters allowing for the shortest attenuation distance. These results could have applications both in the field of acoustic insulation, and for the control of heat transfer.

Nowadays metamaterials are at the focus of an intense research as promising for thermal and acoustic engineering. However, the computational cost associated to the large system size required for correctly simulating them imposes the use of finite-elements simulations, developing continuum models, able to grasp the physics at play without entering in the atomistic details. Still, a correct description should be able to reproduce not only the extrinsic scattering sources on waves propagation, as introduced by the metamaterial microstructure, but also the intrinsic wave attenuation of the material itself. This becomes dramatically important when the metamaterial is made out of a glass, which is intrinsically highly dissipative and with a wave attenuation strongly dependent on frequency. Here we propose a continuum mechanical model for a viscoelastic medium, able to bridge atomic and macroscopic scale in amorphous materials and describe phonon attenuation due to atomistic mechanisms, characterized by a defined frequency dependence. This represents a first decisive step for investigating the effect of a complex nano-or microstructure on acoustic attenuation, while including the atomistic contribution as well.

Nanophononic materials are promising to control the transport of sound in the GHz range and heat in the THz range. Here we are interested in the influence of a dendritic shape of inclusion on acoustic attenuation. We investigate a Finite Element numerical simulation of the transient propagation of an acoustic wavepacket in 2D nanophononic materials with circular or dendritic inclusions periodically distributed in matrix. By measuring the penetration length, diffusivity, and instantaneous wave velocity, we find that the multibranching tree-like form of dendrites provides a continuous source of phonon-interface scattering leading to an increasing acoustic attenuation. When the wavelength is far less than the inter-inclusion distance, we report a strong attenuation process in the dendritic case which can be fitted by a compressed exponential function with β > 1.

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