## Druckverteilungen in granularen Schichten

The findings on the pressure distribution under conical piles has increased the interest in the stress distributions in static granular packings.

Since stresses inside granular systems are very difficult to access experimentally, we have performed DEM (*Discret Element Model*) simulations with polygonal particles. The shape and size of the particles can be specified arbitrarily in the simulation; the influence of these parameters can be determined.

## 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:

## 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.

## Rotation and Reptation

In order to understand the peculiar behavior of granular matter, it is oftenelucidating to observe the physics of only a few grains. We present twosetups which fall into this class: The motion of a single particle in arotating drum, and the collective behavior of a few particles under theinfluence of a swirling motion.

## Schwingungen bei trockener Reibung

A short talk on oscillations with dry friction.

## Spannungsverteilung in Sandhaufen

We are interested in the stress distribution in static granular matter. Experiments have found a **minimum** of the vertical normal stress beneath the apex of a sandpile. Because of the indeterminacy of static friction force even in the simplest sandpile and the ensuing absence of a constitutive relation between stress and strain (Hooke's law) there is no closed set of equations.

## Statik und Dynamik von Aufschüttungen

Granular media conceal a very complex behaviour behind their apparent simplicity ("... is just sand"). Typical properties of granulates are, for example, the discrete structure and the inhomogeneity. This leads to the fact that backfills far away from thermal equilibrium can be very "stable" after all. The question now arises as to what consequences this has for the behaviour of sand accumulations.

## Stress in Static Sandpiles

We are interested in the stress distribution in static granular matter. Experiments have found a **minimum** of the vertical normal stress beneath the apex of a sandpile.

Because of the indeterminacy of static friction force even in the simplest sandpile and the ensuing absence of a constitutive relation between stress and strain (Hooke's law) there is no closed set of equations. Continuum theories, trying to describe the "dip", have to make assumptions on the existence of constitutive relations among the components of the stress tensor itself.