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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.

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In this paper, a numerical model for the prediction of soil-tool interaction forces, based on the Discrete Element Method (DEM) is presented. Three different types of particle-interaction laws for cohesionless, cohesive, and cemented soil are described. The shear strength of the soil is being calibrated by the use of simulated triaxial compression tests. Other parameters of the model are either chosen by experience or by the use of dimensionless numbers. Laboratory tests on a straight cutting blade, which is moved through the sample soil at constant speed, show good agreement with the results of the simulation. For this case, empirical formulas based on the passive earth pressure could be applied. Beyond that, the particle simulation can also be applied in the same manner to more complex tool geometries and trajectories. This is verified by measurements on a wheeled excavator that is working in crushed gravel

A scalar measure, which describes the non-proportionality of local stress paths in engineering applications, is introduced. For this purpose the moment of inertia approach by Meggiolaro is modified in a way that the stress time history is evaluated in a tresca-stress-space. This modification makes the non-proportionality factor invariant with respect to the coordinate system. An optimization procedure is implemented to derive a test setup for new component tests with 2 load channels. The aim of the planned tests is to get a high non-proportionality at the potential crack initiation site. It is not possible to obtain a high non-proportionality factor at the failure location without selective weakening of the component (housing of a rear axle steering). Therefore specific areas of the structure are cut out and the optimization procedure is repeated. As a result of the optimization a test setup with high local non-proportionality at the potential crack initiation site is achieved for the weakened structure. Another setup with slightly less non-proportionality but with a very localized damage is derived. This setup is preferred, because of the robustness in the physical test.