## Ein Simulationssystem für granulare Aufschüttungen aus Teilchen variabler Form

Granular materials, of which sand is the most prominent representative, are important in many fields of research. Their special properties make them important both for industrial applications and as a field of work in basic research. The present work deals with the numerical investigation of granular materials. The size scale of typical granular particles starts in the micrometre range for fine dusts. The upper limit is approximately in the range of a few kilometres particle diameter for the boulders in the rings of Saturn.

## Elastic material properties of sand piles of soft convex poly-gonal particles

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.

## Fast algorithms for the simulation of polygonal particles

Three algorithms to speed up discrete-element simulations for granular matter are presented in this paper. The first algorithm allows to determine neighborhood relations in polydisperse mixtures of particles of arbitrary shape, either discs, ellipses, or polygons. The second algorithm allows to calculate the distance of two polygons in constant time, independently of the complexity of the shape of the polygons. This makes fast simulations of polygonal assemblies possible.

## Funnel I

We have a hopper, filled with about 1300 particles. We can see the funnel-flow of the grains. At the end, two particles on the upper left are stuck.

## Funnel ICA1

A small film showing pattern formation. This was produced for the ICA1 of the University of Stuttgart.

## Funnel II

Now we have the same geometry as in the other funnel, but the shape of the particles was initialized slightly different. The hopper is not blocked.

## Funnel Open Day

A small movie, showing pattern formation. This was produced for the open day of the university 1999 and aims to impress non-scientists. The head which forms is the portrait of Otto von Guericke, Mayor of Magdeburg, who first demonstrated the effect of air pressure via 2 evacuated half-spheres made from iron. The portrait is the seal of the University of Magdeburg. It also demonstrates the versatility of our program.

## Funnel Tina

Penguins, penguins, everywhere are pinguins... A movie for the former supercomputer Tina.

## Galton Board

The Galton Board is a device to explain binomial distributions. It consists of a board that has a large amount of pins fixed to it. These pins are arranged in regular horizontal rows so that the pins form a triangle with its base at the bottom of the board.

## Influence of the geometry on the pressure distribution of granular heaps

We investigate the effect of the geometry of granular heaps on the pressure distribution. For given pressure distributions under cones we compute the pressuredistribution under wedges using linear superposition. For cones with a pressure minimum, the pressure minimum for the corresponding wedge vanishes. Comparisons with experimental data gives good qualitative aggreement, but the total pressure is overestimated.

## Insertion Sort and Closest Features

I want to introduce two algorithms, useful for fast collision detection in granular medium simulations. We all know that the most time consuming part in molecular dynamics simulations is the collision detection. Usually, this problem can be solved by restricting the shape of the particles to spheres. But if you want to use arbitrary convex polygons you need faster algorithms.

At first, a little bit of philosophy:

## Kartenhaus

Dieser Film zeigt den Einsturz eines Kartenhauses. Die Setup-Datei wurde mit Hilfe von xfig erstellt. Ohne die Implementierung eines Gesetzes für Coulomb/statische Reibung wäre die Anfangskonfiguration nicht stabil.

## Maxwells daemon

This setup is shows the behaviour of granular material in a vibrating box. Due to the small wall, the system can break the symmetrie.

## Micro and macro aspects of the elastoplastic behaviour of sand pilesPrimary tabs

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.

## Nichtlineare Schwingungen bei trockener Reibung

The oscillation behaviour of a sliding particle under dry friction in a vertical rotating drum is investigated theoretically. A differential equation is set up for general friction laws. For constant friction coefficients, the equation can be solved exactly. For velocity-dependent friction, it can be treated perturbation theoretically. The unperturbed system is solved and with the help of the averaging method, the perturbed system can then be examined for periodic movements. Different structures of the phase space are found for the different friction laws.

## Nudged hopper

This example shows a hopper with a small outlet and a few large particles. The hopper blocks twice. The clogging is removed by tapping the hopper, so that all particles are accelerated upwards.

## Numerische Simulationen für granulare Medien

Sand is one of the least noticed but almost ubiquitous things in our environment. In physics, too, "simple" sand, or more precisely "granular media", is still a little-studied field. That this is so is due to the complexity hidden in the apparent "simplicity". An analytical solution is self-evident, because the nature of the interaction, friction processes and number of particles form an insurmountable obstacle. But even statistical physics does not yet offer any explanatory models for a pile of sand.

## Open Day

In general, collisions makes granular materials most interesting. For this movie, I tried to avoid collisions!

## Pressure Distribution and stresses under granular heaps with the Distinct Element Method

We investigate the stresses and pressures under a 2-dimensional heap using a simulation of convex polygonal particles. Former Experiments and simulations on granular cones strongly suggest that for cones no generic pressure distribution exists but that the pressure and stress distribution is highly sensitive to the size distribution of the grains and the building history of the heap.

## Rotating Drum

A rotating drum with a mixture of many small and a few large particles.