A Novel Approach to the Simulation of Particles on a Large Size-Range.

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.

Using the averaging method we

• test different friction laws
• search for periodic orbits
• investigate the structure of the phase space

At the present we are interested in better understanding the influence of friction in simulations for granular systems. The far goal is a 3-dimensional simulation for non-spherical particles.

The most time consuming part in molecular dynamics simulations is the collision detection. Usually, this problem is solved by restricting theshape of the particles to spheres. I will present an algorithm, originally developed for virtual reality visualizations by D.Baraff and M.C.Lin, that enables us to use complex polyhedra  (up to 920 faces and more). The expected run time is  O(N), where N is the number of particles in the simulation. Neither complexity nor shape of the particles affect the run time.

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.

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 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.

• What is the pressure distribution below sandpiles? → DIP
• How can I get information from the inside ?
• What can be stated about continuum theories now ?

A Poster on stress propagation in sand beds.