A comparison of Galerkin and streamline techniques for integrating strains from an Eulerian flow field

Two methods are compared for integrating the strains that can arise in finite-element solutions for Eulerian velocity fields associated with large-strain material-forming processes. With the Galerkin formulation, partial differential equations for the deformation gradient are solved over the entire domain based on a weighted residual; with the streamline integrated technique, the corresponding ordinary differential equations are integrated along characteristic lines. Both methods have yielded accurate integrations for the radial-flow and planar-rolling problems studied. A finite-element technique is also presented for ensuring that the free surfaces of the fluid flow are streamlines. This technique has been used for ensuring proper boundary conditions in the rolling analysis.