Object-Oriented Contact Detection Approach for Three-Dimensional Discontinuous Deformation Analysis Based on Entrance Block Theory

Abstract

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 for all blocks, a delicate search phase to detect the four single-contact covers, and an identification phase to identify basic-contact covers from all single-contact covers. Because contacts happen on boundaries of blocks, which can be regarded as a union of boundaries of 3D block angles, the delicate search can be fulfilled through detection between boundaries of 3D block angles to increase its efficiency. After contact detection, a list of potential contact pairs based on the three contact categories was formed and solved based on two basic-contact covers (i.e., vertex-to-face and crossing edge-to-edge contact covers). The half-edge data structure was applied to represent angles, edges, and polygons in polyhedra. The contact detection algorithm was fulfilled in the framework of 3D discontinuous deformation analysis (DDA), using the object-oriented programming method. In this paper, examples are provided to verify the accuracy of the proposed algorithm in treating vertex-to-vertex, vertex-to-edge, parallel edge-to-edge, edge-to-face, and face-to-face contact types as well as its robustness in solving contacts of a large number of blocks.