Polygon-based contact resolution for superquadrics

The representation of discrete objects in the discrete element modelling is a fundamental issue, which has a direct impact on the efficiency of discrete element implementation and the dynamic behaviour of particulate systems. Disks and spheres are the most commonly used geometric shapes due to their geometric simplicity and computational efficiency, but they are unable to provide resistance to rolling motion. For this reason, some non-circular/spherical objects, such as polygons/polyhedrons, superquadrics, or the clustering of disks/spheres to form irregular shapes, are introduced. When superquadrics are used as discrete elements, the bottleneck of contact resolution is associated with the searching for intersections of two non-linear functions, which is a very expensive operation and may sometimes fail in finding the solution. In this work, an efficient and robust algorithm is proposed for contact resolution of 2D superquadrics, in which any superquadric is approximated with a convex polygon through adaptive sampling; then by clipping two polygons, an efficient linear algorithm is performed to search for intersections and overlap area of the polygons; the contact forces and directions are determined by employing a newly established corner/corner contact model. It is important to highlight that the proposed methodology can also be extended to general non-circular discrete object cases. The performance of the algorithm is demonstrated via numerical example