A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation

TL;DR

This paper introduces a comprehensive framework for modeling wave propagation in linear thermo-visco-elastic media, capturing complex behaviors including stress relaxation, dispersion, and interface effects, applicable to solids, fluids, and soft materials.

Contribution

It develops a unified, asymptotic approach to analyze wave dispersion and dissipation in TVE media, integrating interfaces and stress relaxation effects, and connecting to simpler models.

Findings

Asymptotic wavenumber approximations elucidate dispersion characteristics.

Framework effectively models interfaces between fluids and solids.

Stress relaxation significantly influences wave attenuation and scattering.

Abstract

We present a unified framework for the study of wave propagation in homogeneous linear thermo-visco-elastic (TVE) continua, starting from conservation laws. In free-space such media admit two thermo-compressional modes and a shear mode. We provide asymptotic approximations to the corresponding wavenumbers which facilitate the understanding of dispersion of these modes, and consider common solids and fluids as well as soft materials where creep compliance and stress relaxation are important. We further illustrate how commonly used simpler acoustic/elastic dissipative theories can be derived via particular limits of this framework. Consequently, our framework allows us to: i) simultaneously model interfaces involving both fluids and solids, and ii) easily quantify the influence of thermal or viscous losses in a given configuration of interest. As an example, the general framework is applied to the canonical problem of scattering from an interface between two TVE half spaces in perfect contact. To illustrate, we provide results for fluid-solid interfaces involving air, water, steel and rubber, paying particular attention to the effects of stress relaxation.