Differential constitutive equations for polymer melts: The extended Pom–Pom model

The Pom–Pom model, recently introduced by McLeish and Larson [J. Rheol. 42, 81–110 (1998)], is a breakthrough in the field of viscoelastic constitutive equations. With this model, a correct nonlinear behavior in both elongation and shear is accomplished. The original differential equations, improved with local branch-point displacement, are modified to overcome three drawbacks: solutions in steady state elongation show discontinuities, the equation for orientation is unbounded for high strain rates, the model does not have a second normal stress difference in shear. The modified extended Pom–Pom model does not show the three problems and is easy for implementation in finite element packages, because it is written as a single equation. Quantitative agreement is shown with experimental data in uniaxial, planar, equibiaxial elongation as well as shear, reversed flow and step-strain for two commercial low density polyethylene (LDPE) melts and one high density polyethylene (HDPE) melt. Such a good agreement over a full range of well defined rheometric experiments, i.e., shear, including reversed flow for one LDPE melt, and different elongational flows, is exceptional.