Creep relaxation in nonlinear viscoelastic twisted rods

The solution to the problem of stress relaxation in a twisted nonlinear viscoelastic isotropic incompressible rod is presented. We address the multiplicative decomposition of the deformation gradient into reversible (elastic) and irreversible (creep) parts. The elastic potential and the creep potential can be chosen arbitrarily. In particular, the creep law can take into account both the nonlinearity of the relationship between the strain rate and the effective stress, and time-hardening or softening. We consider two variants of creep constitutive relations. One is based on the Tresca equivalent stress, the other is based on the von Mises equivalent stress. The first of them leads to a significant simplification of the governing equations because in this case a radial elastic strain vanishes. In this framework, we obtain a closed-form solution in elementary functions for the coupling of Mooney-Rivlin elastic model and linear creep law. For the von Mises material, numerical-analytical results are obtained. The results are compared with the known small-strain solutions.