Browsing by Author "Brunßen, Stephan"

Now showing 1 - 1 of 1

Open Access
Contact analysis and overlapping domain decomposition methods for dynamic and nonlinear problems
(2008) Brunßen, Stephan; Wohlmuth, Barbara (Prof. Dr.)
This thesis is concerned with the development of efficient numerical schemes for the Finite Element simulation of elastoplastic incremental metal forming processes. Two examples of this new and promising manufacturing technology are introduced to motivate the research work. Some basic technology is provided to accelerate the implicit Finite Element simulation which is still very costly for this kind of operations due to the small but very mobile forming zone and due to the highly nonlinear field equations and inequalities to be solved. For this purpose, the underlying equations and inequalities are reviewed. The main idea to meet these challenges it to use a divide and conquer approach: The workpiece is discretized with a global coarse mesh and the forming zone is meshed with a small fine grid. Unlike in adaptive Finite Elements, no sophisticated remeshing procedures are necessary and the two grids are computationally independent from each other. The interface between coarse and fine computation is small such that a block iterative solution with two different Finite Element programs is possible. To hide the nonlinearities from the global computation, the two meshes interchange information about the plastic deformation and about the contact stresses. Results and algorithms from several disciplines of numerical mathematics and computational mechanics (contact, domain decomposition, iterative solvers, plasticity etc.) are combined to accomplish this task.