  We introduce a class of continuum mechanical models aimed at describing the
behavior of viscoelastic fluids by incorporating concepts originated in the
theory of solid plasticity. Within this class, even a simple model with
constant material parameters is able to qualitatively reproduce a number of
experimental observations in both simple shear and extensional flows, including
linear viscoelastic properties, the rate dependence of steady-state material
functions, the stress overshoot in incipient shear flows, and the difference in
shear and extensional rheological curves. Furthermore, by allowing the
relaxation time of the model to depend on the total strain, we can reproduce
some experimental observations of the non-attainability of steady flows in
uniaxial extension, and link this to a concept of polymeric jamming or
effective solidification. Remarkably, this modelling framework helps in
understanding the interplay between different mechanisms that may compete in
determining the rheology of non-Newtonian materials.
