Formulations of the three-dimensional discontinuous deformation analysis method

This paper extends the original 2D discontinuous deformation analysis (DDA) method proposed by Shi to 3D cases, and presents the formulations of the 3D DDA. The formulations maintain the characteristics of the original 2D DDA approach. Contacts between the blocks are detected by using Common-Plane (C-P) approach and the non-smooth contact, such as of vertex-to-vertex, vertex-to-edge and edge-to-edge types, can be handled easily based on the C-P method. The matrices of equilibrium equations have been given in detail for programming purposes. TheC program codes for the 3D DDA are developed. The ability and accuracy of the formulations and the program are verified by the analytical solutions of several dynamic examples. The robustness and versatility of the algorithms presented in this paper are demonstrated with the aid of an example of scattering of densely packed cubes. Finally, implications and future extensions are discussed.