Adaptive Time Step and Solver for Discrete Element Method - Beam Bond Model

Abstract

This contribution introduces an adaptive strategy for time-stepping and solver selection in simulations based on the Discrete Element Method with beam bond models (DEMBBM). In this approach, particles are connected by virtual beams capable of transmitting axial, shear, and bending forces, enabling the simulation of both discrete and continuum mechanical behaviour. Such capabilities are particularly relevant in crack propagation problems, where an initially continuous structure is progressively disrupted by fracture. While DEM is traditionally solved using explicit or semi-implicit integration schemes, certain classes of DEM-BBM problems, such as those involving progressive fracture, can benefit from implicit methods. These allow for longer time steps without compromising numerical stability. However, the time step size can affect the accuracy of the solution, particularly under rapidly changing conditions. For this reason, it must be continuously adapted based on the current state of the system, with respect to velocities, stress distribution, and oscillatory response. Depending on the state of the system, different solver types can be employed. When the system remains stable and the time step is constant, direct solvers offer high efficiency. In contrast, when frequent structural changes occur, such as during fracture development, iterative solvers are more suitable. The proposed strategy enables dynamic transitions between solver types and time-stepping adaptions, which improves robustness and computational performance.

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