Theoretical Study On Force Transmission And Scaling Law Of Drag Force In Granular Materials

Granular materials are complicated systems which consist of large conglomerations of discrete macroscopic particles. They exist widely in the nature. The behavior of granular medium is hot issues of civil engineering, mechanics and other fields. Since granular matters present peculiar physical properties between solid and fluid, it’s difficult to use traditional continuum mechanic theories to explain these peculiar behaviors. To understand macroscopic mechanical phenomenon of granular, we must analysis behaviors like contacts and collisions from a microscopic perspective. Based on the discrete element method, the paper focus on the quasi-static response of two-dimensional layers to the localized force and the drag force on the intruder in the granular medium. The main work as follows:Firstly, We establish a 2D rectangular composite granular model composed of same-sized particles, and study response of the model under localized force. The results provide a theoretical basis to the force transmission in composite layers.Secondly, based on the discrete method, the drag force on the high-velocity intruder in confined granular bed is investigated, we quantitatively analysis the scaling law of drag force and velocity during the intruder moving through granular medium. The results show that, when the volume fraction on two sides of the jamming transition, the scaling law of drag force and velocity changes qualitatively, the whole dynamic progress presents different physical mechanism. At last we analysis the effects of system parameters like friction coefficient to the scaling law.Finally, in actual engineering fields like geological exploration, the intruder or bit usually accompany with self-induced vibration in the process of drilling. This self-induced vibration would affect the behaviors of surrounding grains, which in turn facilitates the drag force on the intruder or bit varies obviously. Based on second part, the paper investigates the drag on a vibrated intruder in the confined granular medium. And found the effects of amplitude and frequency to drag-velocity relationship.The paper studies on static and dynamic properties of granular materials based on discrete element method. We analysis the peculiar behaviors of granular medium from macroscopic and microscopic perspectives. These results has a significance to geological, physics, chemistry and other actual engineering.