Contact Overlap Calculation Algorithms and Benchmarks Based on Blocky Discrete-Element Method

Abstract

The mechanical response of granular materials has been investigated widely using discontinuous modeling, such as the discrete-element method (DEM). Contact detection and contact resolution have been critical issues when modeling multiple body contacts, especially for arbitrary polyhedral blocks. In this study, the contact overlap calculation algorithms, including polyhedron–polyhedron and polyhedron–boundary contact, were developed to calculate the contact characteristics. For polyhedron–polyhedron contact, the contact overlap volume algorithm is developed based on the geometric dualization theory. The Gilbert–Johnson–Keerthi (GJK) and Quickhull algorithms are used to calculate the overlap polyhedron. The contact characteristics, such as normal direction (n), contact area (a), and penetration depth (un) could be extracted from the contact overlap volume. For polyhedron–boundary contact, a novel and effective algorithm is presented, where the polyhedron–boundary contact is transformed into polyhedron–triangle contact. Then, two types of benchmarks are used to verify the previously mentioned algorithms, which demonstrated that the algorithms could handle the complicated contact types and maintained contact continuity even from face to edge contact. As a complex benchmark, the failure process in a masonry structure is simulated and compared with the model test.