Nowadays, polymers have attracted many researchers due to individual properties in responding to mechanical loadings. According to their time and rate-dependent response to the exterior loads, there was too much complexity to predict mechanical responses. Thus, a thermodynamically consistent viscoelastic-viscoplastic-viscodamage model is considered to predict their mechanical responses. Along with this purpose, the explicit time-discrete form of the constitutive model is used in the finite element software ABAQUS by VUMAT subroutine. This method is valuable since its accuracy, low running time and no need for Jacobian matrix calculations. After validating ABAQUS user subroutine with experimental data obtained from creep, creep-recovery and repeated creep-recovery tests on the polymer, constitutive model sensitivity to the material parameters such as viscoelastic, viscoplastic and damage properties has been investigated. Along with this purpose, it can be observed that increasing viscoplastic and damage parameters could cause rising in the viscoplastic strain and damage variable. Then, the direct effects of loading time and stress level and the indirect effects of unloading time on the polymer strain and damage variable were investigated in the two repeated creep-recovery tests with constant and increasing amplitudes. For instance, doubling the increasing amplitude cycle number from 50 to 100 could rise service life and decrease about 75 percent of damage level.