Lagrangian Finite Element Method for 3D time-dependent viscoelastic flow computation using integral constitutive models

A new technique for the numerical 3D simulation of time dependent flow of viscoelastic fluid is presented. The technique is based on a Lagrangian kinematics description of the fluid flow. The fluid is described by the Rivlin Sawyer integral constitutive equation. The method (referred to as the 3D Lagrangian Integral Method) is a finite element method where Galerkons method is used for solving the governing equation in rectangular coordinates numerically. In the present implementation the velocity and pressure fields are approximated with tri-linear and constant shape functions, respectivly.The 3D LIM has as yet been used to simulate the following two three-dimensional problems. First, the method has been used to simulate the viscoelastic end-plate instability that occurs under certain conditions in the transient filament strecting apparatus for pressure sensitive adhesives (polymeric melts) and polymeric solutions. Secondly, the 3D-LIM has also been applied to calculate the inflation of a thick sheet of a polymeric melt into a elliptic cylinder. These problems all include free surfaces. As the governing equations are solved for the particle positions, the motion of surfaces can be followed easily even in 3D viscoelastic flows.