Time step criterions for nonlinear dense packed granular materials in time-driven method simulations

Discrete-element method (DEM) is a powerful tool for simulations of granular materials. As one branch of DEM,time-driven method (TDM) is suitable for the materials in dense phase. Time step is an important parameter in TDM simulations, which decides the CPU time and the computational accuracy. When a granular system under gravity is deep and nonlinear stress–strain relationship is used to model the particle–particle interaction, some current time step models are not applicable anymore, because the nature frequency of a particle is affected by its boundary conditions. To amend this shortage, a new time step criterion is presented in this paper, which involves the effect from the depth of the system due to gravity. Between this new criterion and that based on Rayleigh time, the smaller one should be the upper limitation of time step in TDM simulations.