Modelling of rheological properties by constitutive equations (CEs) represent a powerful tool for a prediction of the rheological properties of polymer melts and they are crucially important during modelling of the polymer processing (extrusion, injection moulding, thermoforming, blow moulding). Their application allows direct investigation of usually unknown relationships between molecular structures of the polymers and their rheological responses during the modern processes which can be both steady and transient. The CEs represent, of course, only an idealized and simplified form of polymer melt flow description, as it is not possible to achieve a more complete description due to the complexity of the materials and the difficulty of solving numerically the corresponding balance equations. CE together with the continuity equation and equation of motion constitute a standard (unchangeable) form for solving of the numerous problems connected with their processing. A CE completing this set of equations can be proposed in various forms. In the case of viscoelastic liquids (polymeric materials), a CE should respect strong non-linearity caused by a combination of viscous and elastic effects.
The purpose is thus to understand the non-linear rheological behaviour of different polymeric materials and propose the CEs for different class of polymeric materials which respects these nonlinearities (fit and predict these properties with sufficient accuracy) and are also suitable for numerical simulation.