Effects of time integration schemes on discontinuous deformation simulations using the numerical manifold method

Numerical stability by using certain time integration scheme is a critical issue for accurate simulation of discontinuous deformations of solids. To investigate the effects of the time integration schemes on the numerical stability of the numerical manifold method, the implicit time integration schemes, ie, the Newmark, the HHT-alpha, and the WBZ-alpha methods, and the explicit time integration algorithms, ie, the central difference, the Zhai's, and Chung-Lee methods, are implemented. Their performance is examined by conducting transient response analysis of an elastic strip subjected to constant loading, impact analysis of an elastic rod with an initial velocity, and excavation analysis of jointed rock masses, respectively. Parametric studies using different time steps are conducted for different time integration algorithms, and the convergence efficiency of the open-close iterations for the contact problems is also investigated. It is proved that the Hilber-Hughes-Taylor-alpha (HHT-alpha), Wood-Bossak-Zienkiewicz-alpha (WBZ-alpha), Zhai's, and Chung-Lee methods are more attractive in solving discontinuous deformation problems involving nonlinear contacts. It is also found that the examined explicit algorithms showed higher computational efficiency compared to those implicit algorithms within acceptable computational accuracy.