A novel variable fractional constitutive model for complex multistage polymeric behaviors

The mechanical behaviors of glassy polymers, including the viscoelastic and viscoplastic phases, are highly sensitive to temperature and strain rate. In order to describe such complex stress-strain responses, a variable fractional constitutive model considering temperature and strain rate effects is proposed with the order characterized by a biexponential function. Temperature and strain rate dependent criterion are established for both the elastic modulus and relaxation time, which are linearly decreasing functions of temperature. The fractional orders at different temperatures can be described by the same biexponential function, independent of temperature and strain rate, which indicates the same evolution trend during loading. The unloading behavior is subsequently characterized by shifting the order function depending on the reference unload strain. Numerical simulations show that the proposed model well describes and predicts the loading and unloading behaviors of glassy polymers. The physical interpretation of the order evolution is revealed based on the molecular chain mechanism. The validity and applicability of the model is further verified by the application of the model to different glassy polymers.