Bachelor's Thesis

A typical approach of Discrete Element Methods (DEM) is to allow a small overlapping of contacting bodies and use these overlaps to estimate the forces resulting from the collision.

Imagine for example two colliding spheres, drawn as circles in the figure above. Each of these spheres is described by the position of its centre of mass, a radius and a velocity vector defining the direction and rate of the motion of the body. The forces resulting from the collision depend on the length d, which is a measure for the overlap. The direction of the forces are parallel to the so called contact normal, which in this case is the line through the centres of the spheres.

The pe physics engine is a framework for the physically correct simulation of rigid bodies with arbitrary shape. To simulate collisions and body movement the pe makes use of Rigid Body Dynamics based on solvers to handle linear complementary problems.
As DEM are well suited for the interaction of rigid bodies, it is expected, that a DEM-based solver will also work in the pe.

The goal of this thesis is the extension of the Physics Engine (pe) by a Discrete Element method and to compare it to Rigid Body Dynamics in terms of physical correctness and computational efficiency.