A new algorithm for contact detection between convex polygonal and polyhedral particles in the discrete element method

We present an algorithm for contact detection between polygonal (2-D) or polyhedral (3-D) convex particles in the Discrete Element Method (DEM). Noting that the space occupied by a polygon or polyhedron can be defined using a set of linear inequalities, we show that the task of contact detection can be cast as a standard problem in the field of convex optimization, for which there exist established solution procedures. The contact detection algorithm consists of two stages; first to establish intersection and then to calculate the contact point. We can establish intersection between a pair of particles by solving a linear program and, if there is an intersection, use the analytic center of the linear inequalities as the contact point. Once the contact point is obtained, the contact normal can be calculated from the gradient vector of an inner “potential particle” whose corners are rounded (c.f. [13]). The necessary mathematics is presented. Six examples are included to assess the performance of the algorithm in terms of speed and accuracy.