Lagrangian and Arbitrary Lagrangian Eulerian Simulations of Stationary and Non-Stationary Roll Forming Processes

In industry, cold roll forming is more and more used as a manufacturing process mainly for its high productivity and its close geometric tolerances. However, most of the finite element simulations are restricted to the sheet to sheet process - the sheet length being smaller than the whole roll forming line - because the numerical models rely on a Lagrangian kinematics that is not very well suited for the forming of long sheets in a reasonable computational time.
The Arbitrary Lagrangian Eulerian (ALE) formalism, which consists in decoupling the motion of the material and the mesh, has the capability to simulate the continuous process for the whole roll forming line at reduced CPU cost by optimization of the mesh. In the particular case of roll forming, the mesh nodes are fixed in the rolling direction but are free to move in transverse directions. Taking advantage from this approach, the mesh is only refined in the neighbourhoods of the forming tools for accurate modeling of contact and bending.