Implementation of a friction model in an Eulerian viscoplastic formulation for steady flow

The goal of this project was to implement the routines necessary to use the friction model of Wilson and Korzekwa into the finite element analysis program {ital hickory}, in the case of an Eulerian reference frame. {ital hickory} is a deformation simulation code based on finite element modeling of viscoplastic deformation When using {ital hickory}, time-dependent problems are modeled from a Lagrangian reference frame; while steady-state problems are modeled from an Eulerian reference frame. The friction model had been implemented in earlier versions of {ital hickory}, for use with a Lagrangian reference frame. Additional modifications were required, however, to extend this capability to the case of an Eulerian reference frame. That is the subject of this report. The necessary modifications were related to the time integration of the friction state variables. The application of an Eulerian reference frame to study a steady-state flow requires that each specified boundary segment be a streamline of the flow. As such, an initial value for each state variable must be given at the first point of the streamline, and subsequent values must be determined by previous values by integration along the streamline. Additional routines were added to {ital hickory} to implement the streamline integration along the boundary. A plane strain rolling problem was used both to test the implementation and as a source of comparison among friction models