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

Various spatial-gradient extensions of standard viscoelastic rheologies of the Kelvin–Voigt, Maxwell’s, and Jeffreys’ types are analysed 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 modelling aspects is thus revealed in particular selected cases.