An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of eta(o) and tau(t) on M(3.4) were derived from the theory of non-linear viscoelasticity with constraints of entanglements for polymer melts and substituted into the Oldroyed-Walters-Fredickson constitutive equation. An integral constitutive equation for polymer melts was consequently obtained. Some material functions of the constitutive equation related to certain ''test flow'' are examined as follows: (1) simple steady shear flow; (2) steady elongation flow; (3) small-amplitude oscillatory shear flow; (4)stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and compliance). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.
