A novel mixed Eulerian–Lagrangian finite-element method for steady-state hot rolling processes

For the finite-element analysis of steady-state rigid-viscoplastic forming processes in hot rolling of steel, a new and efficient mathematical model was developed. The method is based on a mixed Eulerian–Lagrangian formulation, using an Eulerian co-ordinate in the rolling direction, while employing Lagrangian co-ordinates in the direction of the thickness and width of the strip. This approach leads to an efficient algorithm, where the time is eliminated as an independent variable and the velocity components in the Lagrangian directions are replaced by displacement components as independent field quantities. Due to this concept, the free surface deformations can be accounted for directly and the problems encountered with pure Eulerian or Lagrangian models now appear with reduced complexity and can thus be tackled more easily. The new model is based on a finite-element formulation, modified to account for a mixed treatment of velocity and displacement components.