Constitutive equations for a polymer fluid based on the concept of non-affine networks

Constitutive equations are developed for a polymer fluid, which is treated as a permanent network of strands bridged by junctions. The junctions are assumed to slide with respect to their reference positions under loading. Governing equations are derived by using the laws of thermodynamics under the assumption that the vorticity tensor for the flow of junctions is proportional to that for macro-deformation. Explicit expressions are developed for the steady elongational viscosity, as well as for the steady shear viscosity and normal stress functions. To verify the constitutive relations, three sets of experimental data are approximated on polystyrene solutions with various molecular weights. It is demonstrated that the model can correctly describe stress overshoot for the shear stress and first normal stress difference in start-up tests with various strain rates. Adjustable parameters in the governing equations change consistently with the strain rate, molecular weight and concentration of entanglements. To validate the constitutive equations, observations on low-density polyethylene melt in uniaxial extensional flow are compared with the results of numerical analysis when the material constants are found by matching experimental data in shear tests. Key-words: Polymer fluid, Non-affine network, Stress overshoot, Constitutive equations, Finite deformations