The viscoelastic behavior of thermoplastic polyurethane (TPU) can be described relatively well by linear viscoelastic models in the range of smaller loads (linear region). However, at higher loads, i.e. in the nonlinear region, these models are unable to adequately describe the material. In this case, the Schapery nonlinear constitutive equation is often used, which significantly improves the response prediction but implicitly assumes complete recovery of deformations after unloading. This assumption does not hold for polymeric materials such as TPU. Under cyclic loading, the material exhibits permanent deformations that accumulate and lead to premature product failure. We have extended the aforementioned constitutive equation with a viscoelastic term that enables the modeling of such permanent deformation mechanisms. With proposed experimental-analitical methodology, incorporating creep-recovery measurements at different loading magnitudes and various optimization alghoritems, we have determined the all parameters of the upgraded nonlinear visoelastic-viscoplastic model. Results show that the proposed flow factor (in model) significantly improves prediction of real time-dependent behavior of polymers (error < 4 %), however it has certain limitations under longer periods of loading.
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