Granulare Medien, Paper

By means of molecular dynamic simulation, each individual ballast stone in the ballast track can be simulated in the model.  It is investigated to what extent it is possible to define contact force laws, material parameters and geometry variables in such a way that the resulting computational model reproduces the essential behaviour of the real system. Furthermore, possible areas of application of molecular dynamic simulation are mentioned.

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’’.

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.

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.

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.

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.

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 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.

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.

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.

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 whi ch fall into this class: The motion of a single part icle in a rotating drum, and the collective behavior of a few particles under the influence of a swirling motion.

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.

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.

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.

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.

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.