A novel nonlinear viscous contact model with a Newtonian fluid-filled dashpot applied for impact behavior in particle systems

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Abstract

In this study, we focused on developing a new viscous contact force model by incorporating a novel viscous fluid damping factor derived from the principles of incompressible Newtonian fluid dynamics. This new viscous fluid damping factor was formulated based on the Navier-Stokes equations, providing a robust framework for accurately modeling energy dissipation during impacts. Building on this foundation, a new coefficient of restitution (CoR) model was proposed by integrating the Hertz contact law with the newly developed viscous fluid damping factor. To validate the correctness of the proposed viscous fluid damping factor, a series of experimental data was collected to examine the relationship between the CoR and the impact velocity. The results confirmed the validity of the proposed CoR model and demonstrated that using fluid-based concepts to describe energy dissipation during impacts between solid bodies is feasible and effective. To highlight the advantages of the new viscous contact model, a comparative analysis was conducted against existing viscous contact models. This comparison demonstrated that the new model achieves the highest accuracy in calculating impact behavior, outperforming conventional models. The superior performance of the new model underscores its potential as a powerful tool for studying dynamic interactions in particle systems. The new viscous contact model was further applied to analyze impact behavior in two scenarios: A bouncing ball and a vertical granular chain. In both cases, the results obtained from the model were validated against experimental data, showcasing its ability to capture complex collision dynamics with remarkable precision. In conclusion, our findings establish the new viscous contact force model as an effective and reliable approach for analyzing impact behavior in particle systems. This investigation paves the way for novel approaches to studying energy dissipation during impacts in particle systems by utilizing fluid damping factors instead of the internal damping of particles. The proposed contact force model is applicable to a wide range of dynamic systems involving contact interactions. It is particularly effective for simulating contact events in both flexible and rigid multibody systems. Moreover, the model demonstrates strong performance in granular systems, where frequent collisions, adhesion, and nonlinear contact behaviors are prevalent.

Keywords

viscous fluid damping / Navier-Stokes equations / new contact model / CoR model / particle system

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