A stability condition for an extensive class of viscoelastic motions

The stability problem of viscoelastic solids is usually approached by means of linear integro-differential equations describing infinitesimal perturbed motions. To date, only simple unidimensional problems have been studied and general stability conditions are not available. This paper analyses the case of viscoelastic solids undergoing constant stress under the assumption of fading memory and thermodynamic compatibility. An existence and uniqueness theorem and a stability condition are provided for the problem