AN EXPLICIT CONSTITUTIVE EQUATION FOR PLANE AND AXISYMMETRIC STEADY FLOWS WITH VISCOELASTIC EFFECTS

Abstract

Non-Newtonian materials respond differently when submitted to shear or extension. A
constitutive equation in which the stress is a function of both the rate of deformation and
on the type of the flow is proposed and analyzed theoretically. It combines information
obtained in shear, extension and rigid body motion in all regions of complex flow. The
analysis has shown how to insert some elastic effects in a constitutive equation that depends
only on the present time and position. One advantage of the model is that all the steady
rheological functions in simple shear flow and in extensional flow are predicted exactly.
Another important property that is included is the split of the extensional viscosity in two
parts: one dissipative part that is related to the shear viscosity and an elastic part that is
related to the first and second normal stress coefficients in shear. A discussion involving
the dimensionless numbers that relate elastic and viscosity effects is also given.