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Non-smooth contact dynamics provides an increasingly popular simulation framework for granular material. In contrast to classical discrete element methods, this approach is stable for arbitrary time steps and produces visually acceptable results in very short computing time. Yet when it comes to the prediction of draft forces, non-smooth contact dynamics is typically not accurate enough. We therefore propose to combine the method class with an interior point algorithm for higher accuracy. Our specific algorithm is based on so-called Jordan algebras and exploits the relation to symmetric cones in order to tackle the conical constraints that are intrinsic to frictional contact problems. In every interior point iteration a linear system has to be solved. We analyze how the interior point method behaves when it is combined with Krylov subspace solvers and incomplete factorizations. We show that efficient preconditioners and efficient linear solvers are essential for the method to be applicable to large-scale problems. Using BiCGstab as a linear solver and incomplete Cholesky factorizations, we substantially improve the accuracy in comparison to the projected Gauß-Jacobi solver.

Many components in engineering applications are subjected to multiple and uncorrelated loads during service‐life. Thus, multiaxial stress states with rotating principal axis may occur. For this special case of multiaxial and non‐proportional stresses the results of many fatigue assessment methods which are used in the industrial practice are of poor quality. Fatigue lifetimes of shoulder shafts (quenched and tempered steel) are estimated on the basis of the extended short crack model in combination with a multiaxial notch approximation. This approach shows a high accuracy but the precise modelling of non‐proportional hardening effects requires a complex plasticity model. Therefore, a simplified approach for considering non‐proportional hardening is introduced. Thus, the calculation method gets applicable in the engineering practice. Results are compared to well‐established engineering approaches. Furthermore, new component tests on die‐cast housings with two load channels under constant and variable amplitude loading are presented and discussed. The loads are applied in‐phase (proportional) as well as out‐of‐phase, which results in a high non‐proportional stress path at the crack initiation site. The effects of multiaxial and non‐proportional stress states seem to play a minor role in the fatigue assessment of die‐cast housings.