Applying the Newmark Method to the Discontinuous Deformation Analysis

Discontinuous deformation analysis (DDA) is a newly developed simulation method for discontinuous systems. It was designed to simulate systems with arbitrary shaped blocks with high efficiency while providing accurate solutions for energy dissipation. But DDA usually exhibits damping effects that are inconsistent with theoretical solutions. The deep reason for these artificial damping effects has been an open question, and it is hypothesized that these damping effects could result from the time integration scheme. In this thesis two time integration methods are investigated: the forward Euler method and the Newmark method.

The work begins by combining the Newmark method and the DDA. An integrated Newmark method is also developed, where velocity and acceleration do not need to be updated. In simulations, two of the most widely used models are adopted to test the forward Euler method and the Newmark method. The first one is a sliding model, in which both the forward Euler method and the Newmark method give accurate solutions compared with analytical results. The second model is an impacting model, in which the Newmark method has much better accuracy than the forward Euler method, and there are minimal damping effects.