Lagrangian viscoelastic flow computations using the Rivlin–Sawyers constitutive model

Abstract

A new finite element technique for the numerical simulation of 3D time-dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematics description of the fluid flow. It represents a further development of the 3D Lagrangian integral method (3D-LIM) from an upper convected Maxwell fluid to a fluid described by an integral constitutive equation of the Rivlin–Sawyers type. This includes the K-BKZ model. The convergence of the method is demonstrated on the axisymmetric problem of the inflation of a polymeric membrane only restricted by a clamping ring.