Differential constitutive equations for polymer melts : the extended Pom-Pom model

The Pom-Pom model, recently introduced by Mcleish andLarson [J.Rheol., 42(1), 1998], is a breakthrough in the fieldof visco-elastic constitutive equations. With this model, a correctnon-linear behaviour in both elongation and shear isaccomplished. 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 uniaxia! l, planar, equibiaxial elongation as well as shear, reversed flow and step-strain for two commercial LDPE melts and one 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