Abstract: This paper quantitatively investigates the viscous damping and numerical damping in the discontinuous deformation analysis (DDA) method. The motion equations of the block system are first developed based on the Newmark method; and the relationship among the viscous damping ratio, the dynamic coefficient and the time interval of each step in DDA is developed based on the kinetic theory of viscous damping. The constant acceleration integration scheme in DDA, the partitions and the damping ratio of the numerical damping are discussed; and the calculating formulations of the damping ratio for the combined damping are obtained. An example of the block vibration is analyzed under simple harmonic motions; and the proposed formulations are validated by comparing the DDA calculations to the theoretical solutions. The simulation results show that the viscous damping significantly affects the low frequencies; and the numerical damping can quickly eliminate the interference of the high frequencies. If the two dampings are combined, the frequency-dependence can be reduced. The study results provide a theoretical basis for the vibration and wave calculation using the DDA method.

Key words: discontinuous deformation analysis (DDA), damping problem, Newmark method, viscous damping, numerical damping