Granulare Medien verbergen hinter ihrer scheinbaren Einfachheit ("... ist bloß Sand") ein sehr komplexes Verhalten. Typische Eigenschaften von Granulaten sind zum Beispiel der diskrete Aufbau und die Inhomogenität. Dies führt dazu, daß Aufschüttungen weit entfernt vom thermischen Gleichgewicht doch sehr "stabil" sein können. Es stellt sich nun die Frage, welche Folgen dies für das Verhalten von Sandansammlungen hat.

The problem of granular materials is not alone a problem of material properties, but also a problem of structures. To examine these interesting systems, one uses molecular dynamics simulations. The objective of the work presented here was to have a program which can run on cheap high-end shared memory workstations. Therefore we have developed a fast thread-based simulation of polygonal particles.

The motion of a sliding particle, influenced by friction, in a rotating drum is investigated. A differential equation is formulated for general friction laws. Assuming a constant coefficient of friction, the equation is exactly solvable. For a velocity dependent coefficient of friction, perturbation methods may be used. The nonperturbed system is solved and with the help of the averaging method, the perturbed system can be examined for periodic motions.

We present two-dimensional molecular dynamics simulations of cohesive regular polygons. We investigate the dependence of the angle of respose from the cohesion, which is in good agreement with experiments. Using this as validation, we investigate microscopic parameters which are not accessible to the experiment. This includes contact length, raggedness of the surface and correlation time.

This work is a contribution to the under- standing of the mechanical properties of non-cohesive granular materials in the presence of friction and a continuation of our previous work (Roul et al. 2010) on numerical investigation of the macroscopic mechan- ical properties of sand piles. Besides previous numer- ical results obtained for sand piles that were poured from a localized source (‘‘point source’’), we here consider sand piles that were built by adopting a ‘‘line source’’ or ‘‘raining procedure’’.

We investigate the effective material properties of sand piles of soft convex polygonal particles numerically using the discrete element method (DEM). We first construct two types of sand piles by two different procedures. We then measure averaged stress and strain, thelatter via imposing a 10% reduction of gravity, as well as the fabric tensor. Furthermore, we compare the vertical normal strain tensor between sand piles qualitatively and show how the construction history of the piles affects their strain distribution as well as the stress distribution.

We show how Differential Algebraic Systems (Ordinary Differential Equations with algebraic constraints) in mechanics are affected by stability issues and we implement Lubich’s projection method to reduce the error to practically zero. Then, we explain how the “numerically exact” implementation for static friction by Differential Algebraic Systems can be stabilized. We conclude by comparing the corresponding steps in the “Contact mechanics” introduced by Moreau.

We use a discrete element method to simulate the dynamics of granulates made up from arbitrarily shaped particles. Static and dynamic friction are accounted for in our force laws, which enables us to simulate the relaxation of (two-dimensional) sand piles to their final static state. Depending on the growth history, a dip in the pressure under a heap may or may not appear. Properties of the relaxed state are measured and averaged numerically to obtain the values of field quantitities pertinent for a continuum description.

The effect of the particle shape on the bulk-stress-strain-relations for triaxial compression of granular media is investigated via the molecular dynamicsmethod. It is found that crucial properties exhibited by experimental granular media cannot be reproduced by round particle simulations, but only by theuse of elongated particles.

The pressure distribution under heaps has found to be dependent on the builing hostory of the heap both in experiments and simulations. Up to now, theoretical models and analysis assume that the packing of the heap is homogeneous. We show new experimental and simulational results which indicate that the packing is inhomogeneous and that this packing property is likley causing the pressure minimum under the heap.