Behaviour of the energy density associated to a Kelvin-Voight model in viscoelasticity

We study an initial values problem related to a viscoelasticity model in a periodic medium, with oscillating data at t=0, looking for the homogenization limit of the associated energy density. This limit is determined in a specific case in which there is a constant proportionality between the elastic coefficient and the one in the viscosity part, where it follows an exponential decay in time of the energy density.