Efficient Numerical Simulation of Steady-State Metal Forming Processes by an Iterative Surface Calculation

Abstract

The 3D finite element simulations of processes like multi-pass rolling or drawing often result into exorbitant computational times that make the numerical approach almost infeasible while only the “stationary” step of the process is actually of interest for the industry. Therefore, it can be advantageously simulated by resorting to steady-state formulations which allows reducing the calculation time by, at least, an order of magnitude with respect to more conventional methods where the steady regime is incrementally calculated. A general and robust formulation is developed; it is suitable for parallel computing, compatible with unstructured meshes and general enough to apply to a wide range of forming processes. It consists in alternatively resolving the “simple” steady-state material forming problem for a given domain geometry and then computing the domain corrections that allow satisfying the free surface condition. Within the “simple forming problem”, a Streamline Upwind Petrov Galerkin (SUPG) method is used to integrate the state variables along the streamlines. For the domain geometry correction, a Least Squares formulation with an Upwind shift is introduced. The two resolutions are coupled by the contact equations. This method is applied to several metal forming problems such as 3D rolling and drawing. Results show the high efficiency of the method with respect to an incremental resolution. Computational time is reduced by a factor ranging between 20 and 30. Results are as accurate as with an incremental method. Convergence is always reached whatever the initial geometry of the domain at the beginning of the iterative algorithm.