Irregular polygon shapes (eg, with small edges or small angles) are usually encountered in the contact simulation of discrete block systems. Treatment of irregular polygons in contact detection process has critical effects on the robustness and efficiency of the discontinuous computation approach. The present work proposes a cover‐based strategy to detect and solve contacts of irregular convex polygons in a robust and efficient way. Contact constraints of two polygons are represented by vertex‐edge and edge‐vertex contact covers in 2D. Two loops, namely vertex‐edge loop and edge‐vertex loop, and two filter criteria, namely the entrance filter criterion and the distance filter criterion, are used to establish the potential contact cover list of two neighbor polygons. The initial active and closed contact covers are chosen based on block configuration at the beginning of the step and they are then updated in the open‐close iteration process using proposed criteria. This strategy is implemented in discontinuous deformation analysis. The robustness of the proposed cover‐based approach and the conventional type‐based approach in handling contact of irregular blocks is verified first. Then, the contact analysis efficiency of the cover‐based approach with different contact tolerances is evaluated. This cover‐based method can be extended to 3D case for efficient and robust contact analysis of irregular polyhedral blocks.

Compared with two-dimensional (2D) contact cases, three-dimensional (3D) contact problems are more complicated in both contact geometry representation and contact detection. The entrance block theory proposed by Shi lays the foundation for solving contact problems in a uniform format. This paper presents a new contact detection approach for 3D polyhedral blocks with the use of entrance block theory. In this approach, contacts between 3D polyhedra were classified into three categories: finite-contact covers (face to face, edge to face, and parallel edge to edge), single-contact covers (vertex to face, crossing edge to edge, vertex to edge, and vertex to vertex), and basic-contact covers (vertex to face and crossing edge to edge). A finite-contact cover consists of several single-contact covers, and all single-contact covers can be identified as basic-contact covers. Thus, the contact detection process can be fulfilled in three phases: a rough search phase to form a potential contacting block list f...