Continuum constitutive laws to describe acoustic attenuation in glasses

Abstract

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.

Vibrational density of states of free and embedded semiconducting GaN nanoparticles

“…Note that collective modes involving the full matrix coupled to the nanoparticle are not taken into account by the DM methods due to the fixed condition. It was shown in recent articles that the matrix can also play a role [51], especially from its damping properties [11], together with the impedance break between the particle and the matrix [52]. Collective modes may appear when nanoparticles are embedded in a host matrix.…”

“…Matrix modes are indeed available at those frequencies as can be seen in figure 5 where the SiO 2 VDOS is represented with a dotted line. Previous work showed that, at the interfaces, modes of the different phases combine together [50,51,52]. This effect could be used to deduce which mode can be transmitted or reflected on the inclusion.…”

A continuum model reproducing the multiple frequency crossovers in acoustic attenuation in glasses

“…In Ref. [64], we proposed to use two different simple rheological models for the spherical and deviatoric parts separately, determining the longitudinal and transverse quality factor. Here, we propose a new model for the transverse modes.…”

“…We can write down the full complex constitutive elastic tensor G * [64], which is reduced to a 6 × 6 symmetric matrix due to isotropy, imposing the conditions vi…”

“…Recently, we have proved that the above concept can describe acoustic attenuation in an amorphous material at THz frequencies, in a limited range below the Ioffe-Regel criterium [64]. In that work, we have assumed a constant viscosity, thus leading to a ω 2 behaviour in the acoustic attenuation.…”