Constitutive equations for viscoelastic liquids: Formulation, analysis and comparison with data

Abstract

This chapter discusses the two common classes of viscoelastic constitutive equations (CEs) for polymer melts and concentrated polymer solutions. These are general Maxwell-like and single integral CEs with instantaneous elasticity. The formulation of both classes of CEs are analyzed. The Maxwell-like CEs usually employ some hidden tensor variables with different physical senses. Therefore, in spite of the generality in formulation, their evolution equations and stress relations have different features, depending on the theoretical approach used. Some artifacts related to formulation of the CEs are also exposed. Such an important effect as compressibility is discussed. General results on stability for both classes of CEs is demonstrated, which included stability analyses of both the Hadamard and dissipative types. Results of the stability analyses are applied to popular CEs. The descriptive capability of a class of Maxwell-like CEs is demonstrated, whose formulation satisfies all the stability constraints. The data for equi-biaxial extension is obtained using the lubricated squeezing technique.