Abstract in English:

We present a numerical two-scale simulation approach of the Nakajima test for dual-phase steel using the software package FE2TI, a highly scalable implementation of the well known homogenization method FE². We consider the incorporation of contact constraints using the penalty method as well as the sample sheet geometries and adequate boundary conditions. Additional software features such as a simple load step strategy and prediction of an initial value by linear extrapolation are introduced. The macroscopic material behavior of dual-phase steel strongly depends on its microstructure and has to be incorporated for an accurate solution. For a reasonable computational effort, the concept of statistically similar representative volume elements (SSRVEs) is presented. Furthermore, the highly scalable nonlinear domain decomposition methods NL-FETI-DP and nonlinear BDDC are introduced and weak scaling results are shown. These methods can be used, e.g., for the solution of the microscopic problems. Additionally, some remarks on sparse direct solvers are given, especially to PARDISO. Finally, we come up with a computationally derived Forming Limit Curve (FLC).