Fractional calculus description of non-linear viscoelastic behaviour of polymers

In recent decades, constitutive equations for polymers involving fractional calculus have been the object of ever increasing interest, due to their special suitability for describing self-similarity and memory effects, which are typical of viscoelastic behaviour in polymers. Thermodynamic validity of these equations can be ensured by obtaining them from analog models containing spring-pots with positive front factors. Failure of self-similarity in real polymers at short (local) and long (whole chain) scales has been addressed previously. In the past, interest in fractional differential descriptions of polymer viscoelasticity has been mainly concerned with linear viscoelasticity, despite the fact that in processing and end use conditions are largely in the non-linear range. In this paper, extension of fractional calculus models to the non-linear range of viscoelasticity is attempted, by accounting for stress activation of deformation and strain acceleration of annealing. Calculated stress-strain curves are compared with experimental results on an amorphous polymer (polycarbonate). The model adequately describes the general trends of yield and post-yield behaviour, but does not properly describe the gentle approach to yield observed experimentally.