Creep, recovery and vibration of an incompressible viscoelastic material of the rate type: Simple tension case

We consider three-dimensional nonlinear viscoelastic models that account for both stress relaxation and creep/recovery phenomena. These are based on different frame indifferent time derivatives: the Oldroyd (or upper-convected) derivative, Jaumann co-rotational) derivative Cotter–Rivlin lower-convected) derivative. Under a simple tension creep process, these constitutive equations predict same but lead to situations. The lower-convected require restrictions values of material parameters as well traction/compression stress. model derivatives does not any restriction. All examined used study finite amplitude, horizontal oscillatory motion mass attached rate-type string. In this way we generalize classical results by Beatty Zhou (1991).