General nonlocal Kelvin-Voigt viscoelasticity: application to wave propagation in viscoelastic media

In this paper, we develop a new relaxation model that accounts for the nonlocal fields of Kelvin-Voigt viscoelastic materials and assumes different nonlocal-attenuations of the material's elastic and viscous properties. The new relaxation model is then implemented to study the influence of the nonlocal, non-neighbor interactions on the wave propagation in viscoelastic media, while elucidating how the contrast between longitudinal and transverse nonlocal fields contributes to the dispersion of the propagating waves. The numerical results reveal two mechanisms of viscoelastic wave damping, as in addition to the viscosity-which is an explicit wave damping-viscoelastic waves are also damped implicitly by the nonlocal effect. We therefore foresee that the new relaxation model will be used for the design of non-reciprocal and non-Hermitian material systems.

Automated summary

In this paper, a new relaxation model that considers the nonlocal fields of Kelvin-Voigt viscoelastic materials is developed. The model investigates the influence of nonlocal, non-neighbor interactions on wave propagation in viscoelastic media and examines the contrasting effects of longitudinal and transverse nonlocal fields on wave dispersion. The numerical results reveal two mechanisms of wave damping in viscoelastic materials, namely explicit damping caused by viscosity and implicit damping caused by nonlocal effects.