Three-dimensional discontinuous deformation analysis (3-D DDA) method for particulate media applications

This paper presents a new numerical model for simulation of granular materials consisting of 3-D spheres bounded by rigid boundaries. The proposed model is based on Three-Dimensional Discontinuous Deformation Analysis (3-D DDA), a numerical method recently developed for simulation of particles in motion. Stiffness and force matrices due to body forces, point loading, inertia forces, and displacement and directional constraints are derived in detail. Moreover, an efficient model for particle contacts in 3-D is presented. In this model, sphere-sphere and sphere-boundary contacts are simply transformed into the form of point-to-plane contacts. Normal and shear contact forces as well as friction force for both sphere-sphere and sphere-plane contact types are derived by vector analysis and the penalty method. The numerical model developed herein is a simple and efficient method that can be easily coded into a computer program. The validity and capability of the model are demonstrated by numerical results obtained for several illustrative examples. Furthermore, some examples are presented and discussed to illustrate the application of the 3-D DDA to particulate media.