The dynamics of concentrated polymers of high molecular mass is domina
ted by topological interactions (or entanglements). The nonlinear effe
cts shown by these systems in fast flows are still poorly understood,
however. We have recently noted that a mechanism of convective constra
int release should play a significant role in the nonlinear range, and
preliminary calculations have been made both for a simple dumbbell mo
del and for the tube model of Doi and Edwards. Here we show that furth
er elaboration of the simple dumbbell model can predict quite complex
rheological behaviours such as those observed dy Navard and coworkers
in semi-dilute solutions of ultrahigh molecular mass polymers.