Highly Stable Explicit Temporal Integration for Discrete Element Computations

This paper presents the adaptation of a semi-implicit time integration scheme that has been reported in the literature and its implementation for use in discrete element methods (DEM). The computational efficiency of DEM methods is primarily associated with the selection of time increment sizes, as dictated by stability requirements, and other factors that depend on the particulars of the DEM implementation and the problems solved. The proposed time integration scheme and the associated DEM are developed for problems pertaining to rigid-particle interaction and interaction of elastic bodies that are modeled as a cluster of rigid interconnected particles. Verification studies that consider nonlinear problems demonstrate that the proposed algorithm is unconditionally stable and accurate even for large time step sizes and when applicable does not require any inversions of the system matrices. Assessment studies on the accuracy, stability, and computational efficiency of the method have been conducted and discussed. The implementation of the proposed method is discussed and demonstrated through a showcase problem.