Some remarks about a simple history dependent nonlinear viscoelastic model

A simple model for history dependent nonlinear viscoelasticity is considered. The determining equation governing shear motions is derived and investigated in the quasistatic approximation and under the traveling waves ansatz. Traveling waves are possible only if an inequality involving the constitutive parameters is satisfied. This fact is in contrast to what happens in viscoelasticity of the Kelvin-Voigt type. On the other hand, in the quasi-static approximation (classical creep and recovery experiments) the behavior of the history dependent model is similar to analogous rate dependent models.