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

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.