A micro-inertia gradient visco-elastic motivation for proportional damping

In this paper, a micro-inertia gradient visco-elasticity theory is proposed and implemented for the description of wave dispersion in periodic visco-elastic composites characterised by (stiffness-)proportional damping. An expression for the internal length parameter has been derived in terms of geometry and material properties. The theory has been validated through a numerical simulation of wave propagation in a one-dimensional periodic composite bar for two different heterogeneity levels, where the proposed theory has shown good agreement with the solution obtained by explicitly modelling the material heterogeneity. The effects of both gradient enrichment and viscosity on wave propagation as well as their interaction have also been analysed.