Some gradient theories in linear visco-elastodynamics towards dispersion and attenuation of waves in relation to large-strain models

TL;DR

This paper explores gradient extensions of classical viscoelastic models to understand wave dispersion and attenuation in linear and large-strain nonlinear contexts, revealing their interconnected roles in wave propagation analysis.

Contribution

It introduces and analyzes spatial-gradient extensions of standard viscoelastic rheologies in both linear and nonlinear large-strain models, clarifying their roles in wave propagation.

Findings

Gradient models affect wave dispersion and attenuation.

Large-strain models use gradient extensions for analytical purposes.

Interconnection between linear and nonlinear gradient models is established.

Abstract

Various spatial-gradient extensions of standard viscoelastic rheologies of the Kelvin-Voigt, Maxwell's, and Jeffreys' types are analyzed in linear one-dimensional situations as far as the propagation of waves and their dispersion and attenuation. These gradient extensions are then presented in the large-strain nonlinear variants where they are sometimes used rather for purely analytical reasons either in the Lagrangian or the Eulerian formulations without realizing this wave-propagation context.The interconnection between these two modeling aspects is thus revealed in particular selected cases.