Virtual Element Method for Cross-Wedge Rolling during Tailored Forming Processes

Abstract In this work we present an application of the virtual element method (VEM) to a forming process of hybrid metallic structures by cross-wedge rolling. The modeling of that process is embedded in a thermomechanical framework undergoing large deformations, as outlined in [1, 2]. Since forming processes include mostly huge displacements within a plastic regime, the difficulty of an accurate numerical treatment arises. As shown in [3], VEM illustrates a stable, robust and quadratic convergence rate under extreme loading conditions in many fields of numerical mechanics. Numerically, the forming process is achieved by assigning time-dependent boundary conditions instead of modeling the contact mechanics yielding to a simplified formulation. Based on the two metallic combinations of steel and aluminum, different material properties are considered in the simulations. The purpose of this contribution is to illustrate the effectiveness of such a non-contact macroscopic framework by employing suitable boundary conditions within a virtual element scheme. A comparison with the classical finite element method (FEM) is performed to demonstrate the efficiency of the chosen approach. The numerical examples proposed in this work stem out from the DFG Collaborative Research Centre (CRC) 1153 “Process chain for the production of hybrid high-performance components through tailored forming”.