INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2009; 77:1224–1246 Published online 4 September 2008 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.2450 An overlapping domain decomposition method for the simulation of elastoplastic incremental forming processes Stephan Brunssen ∗, † and B. Wohlmuth Institut f¨ ur Angewandte Analysis und Numerische Simulation (IANS), Universit¨ at Stuttgart, 70569 Stuttgart, Germany SUMMARY The implicit finite element (FE) simulation of incremental metal cold forming processes is still a chal- lenging task. We introduce a dynamic, overlapping domain decomposition method to reduce the compu- tational cost and to circumvent the need for sophisticated remeshing procedures. The two FE domains interchange information using the elastoplastic operator split and the mortar method. Copyright 2008 John Wiley & Sons, Ltd. Received 8 August 2007; Revised 25 March 2008; Accepted 15 July 2008 KEY WORDS: coupled problems; forming processes; domain decomposition; two-scale; elastoplasticity; mortar method; solids; finite elements; plasticity; metal forming; multiscale 1. INTRODUCTION A motivation is given in this section and the main challenges and solution methods are introduced. 1.1. Challenges Deep rolling of turbine blades [1], see Figure 1, is a recently introduced forming technique, using simple shaped, small and flexible tools. This process is employed to counteract the weakening of fatigue strength by treating the surface of the component in such a way that hardening and residual compressive stresses are introduced. The design of deep-rolling processes is very difficult since up to now no methods exist for deriving the tool path from the desired workpiece properties. ∗ Correspondence to: Stephan Brunssen, Institut f¨ ur Angewandte Analysis und Numerische Simulation (IANS), Universit¨ at Stuttgart, 70569 Stuttgart, Germany. † E-mail: brunssen@ians.uni-stuttgart.de Contract/grant sponsor: German Research Foundation (DFG); contract/grant number: WO671/4-1 Copyright 2008 John Wiley & Sons, Ltd.