Continuum Mech. Thermodyn. (2005) 17: 217–246 DOI 10.1007/s00161-004-0200-6 ORIGINAL ARTICLE A. D. Drozdov · M. Gottlieb Constitutive equations for non-affine polymer networks with slippage of chains Received: 19 November 2004 / Accepted: 9 December 2004 / Published online: 25 May 2005 C  Springer-Verlag 2005 Abstract A model is derived for isothermal three-dimensional deformation of polymers with finite strains. A polymer fluid is treated as a permanent network of chains bridged by junctions (entanglements). Macro- deformation of the medium induces two motions at the micro-level: (i) sliding of junctions with respect to their reference positions that reflects non-affine deformation of the network, and (ii) slippage of chains with respect to entanglements that is associated with unfolding of back-loops. Constitutive equations are developed by using the laws of thermodynamics. Three important features characterize the model: (i) the symmetry of relations between the elongation of strands and an appropriate configurational tensor, (ii) the strong nonlinear- ity of the governing equations, and (iii) the account for the volumetric deformation of the network induced by stretching of chains. The governing equations are applied to the numerical analysis of extensional and shear flows. It is demonstrated that the model adequately describes the time-dependent response of polymer melts observed in conventional rheological tests. Keywords Polymer fluids · Non-affine networks · Chain stretching · Constitutive equations · Viscoplasticity 1 Introduction This paper deals with modeling the time-dependent response of dense polymer fluids (melts and concentrated solutions) at finite strains. Although this subject has been a focus of attention in the past three decades, it is difficult to mention constitutive equations that adequately describe the characteristic features of the viscoelas- tic behavior of polymer fluids observed in extensional and shear flows, on the one hand, and that are relatively simple for their numerical implementation, on the other. Conventional constitutive equations for polymer fluids based on the concept of non-affine networks [1–4] presume that strands in a network are rigidly connected with junctions, whereas the junctions can slide with re- spect to their positions in the bulk medium. An important advantage of this approach is that the sliding process is described by ordinary differential equations (whose form is determined by appropriate kinematic hypothe- ses), which implies that the governing equations can be implemented for numerical simulation of flows in do- mains with complicated geometries. Another advantage of these models is that they do not distinguish between flows of dense and dilute polymer systems, because, from the physical standpoint, deformation of a strand be- tween entanglements in a polymer melt is treated in the same way as deformation of a chain in a dilute polymer solution. This allows such phenomena as strain hardening in transient extensional flows and stress overshoot in start-up shear flows (which are observed experimentally in solutions, as well as in melts) to be described Communicated by S. H. Faria A. D. Drozdov (B ) · M. Gottlieb Department of Chemical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel E-mail: aleksey@bgumail.bgu.ac.il