A streamline element scheme for solving viscoelastic flow problems. Part I. Differential constitutive equations

Abstract

A finite element program for solving viscoelastic flow problems in plane and axisymmetric geometries is described. The program is based on a streamline element scheme (S.E.S.). One of the principal features of the program is that it employs an iterative process to treat elastic stresses as pseudo-body forces; during each iteration it generates updated streamline-based elements and integrates Maxwell-type constitutive equations along the streamlines forming the element boundaries. The performance of this method was satisfactory, considering both accuracy and efficiency. Results of two simple test problems and two complex flow problems are shown. These problems are simple shearing flow, uniaxial and biaxial elongation, extrudate swelling and flow around a sphere in a long cylinder. In the simple test problems the results were very accurate and were compared with exact solutions and inthe more complex flows the results were in close agreement with data from other programs based on different methods. Some limitations and the current state of development of the program are also discussed.