Discontinuous Deformation Analysis - DDA Vs DEM

DDA Vs DEM

Although DDA and DEM are similar in the sense that they both simulate the behavior of interacting discrete bodies, they are quite different theoretically. While DDA is a displacement method, DEM is a force method. While DDA uses displacement as variables in an implicit formulation with opening-closing iterations within each time step to achieve equilibrium of the blocks under constrains of the contact, DEM employs an explicit, time marching scheme to solve the equations of motion directly (Cundall and Hart, 1989). The system of equation in DDA is derived from minimizing the total potential energy of the system being analyzed. This guarantee that equilibrium is satisfied at all times and that energy consumption is natural since it is due to frictional forces. In DEM, unbalanced forces drive the solution process, and damping is used to dissipate energy. If a quasi-static solution is desired in which the intermediate steps are not of interest, the type of damping and the type of relaxation scheme can be selected in DEM to obtain the most efficient solution method (Cundall, 1987). The application of damping in DEM for quasi-static problem is somewhat analogues to the setting to zero of the initial velocities of the block in the static analysis of DDA. In dynamic problem, however, the amount and type of damping in DEM, which are very difficult to qualify experimentally, has to be selected very carefully to as not to damp out real vibrations. On the other hand, the energy consumption in DDA is due to the frictional resistance at contact. By passing the velocities of the blocks at the end of a time step to the next time step, DDA gives real dynamic solution with correct energy consumption (Shi, 1988). By using an energy approach, DDA does not require an artificial damping term to dissipate energy as in DEM, and can easily incorporate other mechanisms for energy loss.