© 2016 John Wiley & Sons, Ltd. Quasi-static elastoplastic contact problems are ubiquitous in many industrial processes and other contexts, and their numerical simulation is consequently of great interest in accurately describing and optimizing production processes. The key component in these simulations is the solution of a single load step of a time iteration. From a mathematical perspective, the problems to be solved in each time step are characterized by the difficulties of variational inequalities for both the plastic behavior and the contact problem. Computationally, they also often lead to very large problems. In this paper, we present and evaluate a complete set of methods that are (1) designed to work well together and (2) allow for the efficient solution of such problems. In particular, we use adaptive finite element meshes with linear and quadratic elements, a Newton linearization of the plasticity, active set methods for the contact problem, and multigrid-preconditioned linear solvers. Through a sequence of numerical experiments, we show the performance of these methods. This includes highly accurate solutions of a three-dimensional benchmark problem and scaling our methods in parallel to 1024 cores and more than a billion unknowns.
|Original language||English (US)|
|Number of pages||24|
|Journal||International Journal for Numerical Methods in Engineering|
|State||Published - Aug 6 2015|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: Parts of the work of the first author were supported by the Deutsche Forschungsgemeinschaft (DFG) within Priority Program 1480, ‘Modelling, Simulation and Compensation of Thermal Effects for Complex Machining Processes’, through grant number BL 256/11-3.The third author is supported by the National Science Foundation through award no. OCI-1148116. The second and third authors are supported in part by the Computational Infrastructure in Geodynamics initiative (CIG), through the National Science Foundation under award no. EAR-0949446 and The University of California—Davis. This publication is based in part on the work supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).Some computations for this paper were performed on the Brazos and Hurr clusters at the Institute for Applied Mathematics and Computational Science (IAMCS) at Texas A&M University. Part of Brazos was supported by NSF award DMS-0922866. Hurr is supported by award no. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.