Explicit Three Dimensional Discontinuous Deformation Analysis for Blocky System

We present a 3D-DDA formulation that uses an explicit time integration procedure and an efficient contact detection algorithm optimized to minimize the computational effort. The advantages of the explicit formulation are that the global stiffness matrix does not need to be assembled and the linear equations do not need to be solved by matrix inversion. Consequently, the computational effort and memory requirement can be reduced considerably, which is important for efficient solution of large 3D problems. In addition, the computational efficiency is increased by eliminating unnecessary contact computations using a grid based nearest neighbor search. The grid divides space into a number of cells of equal size and each object is then associated with the cells it overlaps. As only objects overlapping a common cell can possibly be in contact, in-depth tests are only performed on objects found sharing cells with the block tested for collision. The contacts between the blocks are detected by using Fast Common- Plane (FCP) approach. The halfedge (HE) data structure approach is used to handle the navigation into the topological information associated with polyherdral objects (vertices, edges, faces). The halfedge data structure allows for quick traversal between faces, edges, and vertices due to the explicitly linked structure of the network. Examples are provided which demonstrate the capabilities of new algorithm and the size of problem that can be analyzed.