Project Description

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In this work the collective dynamical behaviour of many convex and non-convex polyhedral bodies in space is of interest. To be able to simulate a high number of bodies, methods from Molecular Dynamics (MD) are frequently used. Here these methods are combined with collision detection methods and contact formulations adopted from Multibody Systems (MBS).

Originally in MD molecules are considered and it is the goal to describe their interactions and their collective behaviour. These interactions depend on macroscopic measurable properties of the materials, e.g. viscosity or elasticity. In such systems, where the dynamical behaviour is calculated on the scale of the molecules, a very high number of particles is investigated. In order to simulate such a high number of bodies, in MD the molecules are often modelled by rigid spheres. The material behaviour is then represented by the forces that are acting between the bodies. In MD such forces can be attractive forces like Van der Waals forces, but they can also be contact forces that are applied to a colliding molecule pair. To calculate the forces effectively, overlaps between the particles are accepted, and the value of the force depends on the distance between the colliding bodies. Such methods for the calculation of contact forces are also called constitutive methods. The constitutive laws from MD are here applied to three dimensional solid bodies of different shape.

Simulations of granular material or bulk solids are based on free bodies in space. In the space a free body has six degrees of freedom. Then, the equations of motion can be obtained easily taking into account three elementary rotations for example the Kardan-angles and three translational degrees of freedom. After neighbouring body pairs have been found the time consuming collision detection for polygonal convex or non-convex bodies can be accomplished. For the colliding bodies contact forces have to be computed. To apply the contact force to the bodies, the contact geometry has to be detected. For spherical bodies, this contact geometry is quite simple, e.g. the normal contact force simply acts in radial direction to the surface of the body. Here, more complex geometries are considered and the relevant surface part has to be found out. The resulting forces and moments acting on each body must then be incorporated into the equations of motion.

Related Pages

• References to granular media and publications at Stefan Luding's homepage.

Contact

• Dipl.-Ing. Beate Muth