Granular matter hides a very complex behaviour behind its 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.

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 present two-dimensional molecular dynamics simulations of cohesive regular polygonal particles. The cohesive part of the force-law for the particleparticle interaction is validated by the agreement with existing experimental data. We investigate microscopic parameters which are not accessible to experiments such as contact length, raggedness of the surface and correlation time. With increasing cohesion the particles move in clusters for long times.

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.

In order to understand the peculiar behavior of granular matter, it is often elucidating to observe the physics of only a few grains. We present two setups which fall into this class: The motion of a single particle in a rotating drum, and the collective behavior of a few particles under the influence of a swirling motion.

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.

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.

We investigate the effect of the geometry of granular heaps on the pressure distribution. For given pressure distributions under cones we compute the pressure distribution 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 agreement, but the total pressure is overestimated.

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.

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.