Modeling of nonlinear viscoelasticity at large deformations

A constitutive model of finite strain viscoelasticity, based on the multiplicative decomposition of the deformation gradient tensor into elastic and inelastic parts, is presented. The nonlinear response of rubbers, manifested by the rate effect, cycling loading and stress relaxation tests was captured through the introduction of two internal variables, namely the constitutive spin and the back stress tensor. These parameters, widely used in plasticity, are applied in this work to model the nonlinear viscoelastic behaviour of rubbers. The experimental results, obtained elsewhere, related with shear deformation in monotonic and cyclic loading, as well as stress-relaxation, were simulated with a good accuracy.