A new hysteretic damping model and application for the combined finite-discrete element method (FDEM)

In the field of mechanical numerical simulation, damping is always a vital parameter. However, in the combined finite-discrete element method (FDEM), the current application of damping is insufficient. Therefore, in this paper, a new hysteretic damping model and its corresponding critical damping coefficient acquisition method are proposed. Furthermore, simulations of quasi-static tunnel excavation and quasi-dynamic rock slope slip are employed to investigate the influence of different hysteretic damping ratios on the numerical results. The study results show that the new hysteretic damping model, which is independent on the calculation time step, considers the effects of the element size, Young's modulus and material density and can obtain the critical damping coefficient by comprehensively using cantilever beam vibration numerical modelling and theoretical equations. In addition, the sensitivity of quasi-static tunnel excavation to the hysteretic damping ratio is very weak; however, for quasi-dynamic rock slope slip simulation, the damping ratio eta has a substantial influence on the simulation results. The new hysteretic damping model proposed in this paper is important for improving the accuracy of FDEM numerical simulation results, especially for quasi-dynamics simulation.