A simple model of nonlinear viscoelasticity taking into account stress relaxation

We present one of the simplest theory of nonlinear viscoelasticity taking into account stress relaxation. The model is a 3D nonlinear generalization of the standard three-parameter model of 1D classical viscoelasticity. In the framework of this theory, we examine some simple deformations. First of all, we consider a homogeneous deformation as a possible idealization of the usual triaxial test. By this analysis, we show that the model under investigation may be interesting to describe the mechanical behavior of materials like bitumen and hot mix asphalt. Moreover, we investigate the evolution of shearing motions (mainly in the quasi-static approximation) to point out several aspects of the rich mechanical response of constitutive theories in implicit form.