Fully-coupled micro–macro finite element simulations of the Nakajima test using parallel computational homogenization

Abstract The Nakajima test is a well-known material from the steel and metal industry to determine forming limit of sheet metal. It demonstrated how FE2TI, our highly parallel scalable implementation computational homogenization method FE $$^2$$ 2 , can be used for simulation test. In this test, sample geometry clamped between blank holder die. Then, hemispherical punch driven into specimen until failure occurs. For software package FE2TI has been enhanced with frictionless contact formulation on macroscopic level using penalty method. appropriate choice suitable boundary conditions as well influence symmetry assumptions regarding symmetric setup are discussed. order able solve larger problems more efficiently, balancing domain decomposition by constraints (BDDC) approach implemented an alternative sparse direct solver. To improve efficiency even further, additionally, adaptive load step different extrapolation strategies compared. Both yield significant reduction overall computing time. Furthermore, strategy dynamically increase parameter presented which allows resolve accurately without increasing time too much. Numerically computed diagrams based virtual tests presented.