Continuum Modelling and Simulation for Viscoelastic Materials

Abstract

A class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity is introduced. 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. Numerical simulations are presented to further illustrate the properties of the proposed model.