A robust algorithm for ellipse-based discrete element modelling of granular materials

With recent research indicating the importance of the rolling mechanism of deformation in granular systems consisting of perfectly round particles, it has become popular to use ellipse-shaped particles in the Discrete Element Method (DEM) numerical model. Inherent in this technique is the need for accurately computing ellipse to ellipse intersection, in order to properly detect contact formation and compute relative contact velocities. However, the commonly used algorithms for computing ellipse-ellipse intersection are generally poorly conditioned and can be inaccurate. An alternate method for computing ellipse-ellipse intersection is developed and presented which results in a well-conditioned, stable and accurate contact detection method. These modification are incorporated into the general DEM algorithm.