A simple integral constitutive equation for polymeric liquids

An integral constitutive equation describing the strain history in terms of the Cauchy-Green and Finger tensors is presented. Its memory functions, which correspond to a flow-dependent continuous spectrum of relaxation times, depend on the invariants of the Cauchy-Green and Finger rate of strain tensors. Theoretical predictions resulting from this equation are compared with experimental data for some types of flow. Using the Laguerre polynomial expansion, the basic equation is generalized.