Modelling & Simulation


FE2TI: Computational Scale Bridging for Dual-Phase Steels

Axel Klawonn, Universität zu Köln, Köln, Germany
Martin Lanser, Universität zu Köln, Köln, Germany
Oliver Rheinbach, TU Bergakademie Freiberg, Freiberg, Germany

Advanced High Strength Steels (AHSS) provide a good combination of both strength and formability and are therefore applied extensively in the automotive industry, especially in the crash relevant parts of the vehicle. Dual-phase (DP) steel is an example for such AHSS which is widely employed. The excellent macroscopic behavior of this steel is a result of the inherent micro-heterogeneity and complex interactions between the ferritic and martensitic phases in the microstructure. Thus, considering the microscale is indispensable for realistic simulations.

In order to bring large micro-macro simulations to modern supercomputers, we combine the well-known FE2 scale bridging approach with a highly scalable implementation of the FETI-DP domain decomposition method (Finite Element Tearing and Interconnecting - Dual Primal), which is used as a solver on the microscale. This results in our highlyscalable software FE2TI. In FE2, in each Gauss integration point of the macroscopic problem, a microscopic problem is solved on a representative volume element (RVE). The incorporation of the microscale replaces a phenomenological material law on the macroscale.

The MPI-parallel C/C++ implementation uses PETSc, and efficient solver packages such as BoomerAMG, MUMPS, and UMFPACK are interfaced. The different RVEs are independent of each other, coupled only through the macroscopic problem and thus can be solved in parallel. In our approach, each RVE is assigned to its own MPI communicator and solved using an inexact-reduced FETI-DP variant. In these highly scalable FETI-DP variants (up to 786,432 BG/Q cores on Mira, Argonne National Laboratory, USA) the FETI-DP coarse problem is solved inexactly using an AMG (algebraic multigrid) method. Weak scalability results for different three-dimensional nonlinear, micro-heterogeneous hyperelasticity problems are presented, scaling up to the complete JUQUEEN (458,752 BG/Q cores) at FZ Jülich and the complete Mira (786,432 BG/Q cores) at Argonne National Laboratory, USA.

The FE2TI approach is used in the project ”EXASTEEL - Bridging scales for multiphase steels” within the first funding period of the DFG priority program SPP 1648 ”Software for Exascale Computing” (SPPEXA). It will be further developed in the second funding period of SPPEXA within the project ”EXASTEEL-2: Dual-Phase Steels - From Micro to Macro Properties”.

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