A unified constitutive theory for polymeric liquids I. Basic considerations and a simplified model

By combining a continuum mechanical approach with considerations of network theory and thermodynamics of irreversible processes, a set of differentialtype constitutive equations for polymeric liquids are obtained which provide expressions for the stress tensor, evolution equations of the effective Finger strain and Cauchy strain for the network deformation, and a first order differential equation governing the rigidity modulus. Unlike Giesekus' recent unified approach that starts from the bead-spring model, the theory lends itself more readily to a better understanding of most of the current theories based on continuum mechanics and molecular network concepts. Different recent models such as those due to Leonov, Dashner—Van Arsdale, Phan Thien—Tanner, and Acierno et al. (or Marrucci) can be unambiguously interpreted as resulting from specific approximations or additional assumptions.