Study Of Contact Algorithm For 3-d Discrete Element Method

Granular substance is common in the real world, which is often composed of a large number of interactive discrete particles. It has very complicated response characters under loading, although the mechanical behavior of its component paticle is very simple. In some circumstances it act as solid, in other cases it flows like liquid. This is due to the conatct effects between particles and its material discontinuity. Thus, classic theory of continuum mechanics can't be readily utilized for this kind of material.The discrete element method (DEM) is an efficient numerical means to study granular material, in which the contact algorithm is the sticking point. In simulating the response of a big bulk of discrete material composed of many particles, the processes of contact detection and contact force updating is quite time consuming. As a result, the DEM computation efficiency and precision heavily rely on the contact algorithm. It has indicated that for three-dimensional particles with complicated shapes, contact handling operations takes up more than 80 percent of the whole computational time. Thus, it is widely recognized that DEM contact algorithm plays an extremely important role in simulation of granular material.firstly, this paper proposes an algorithm to generate three-dimensional arbitrary polyhedral model for the discrete particles. The initial collisions among particles are avoided by introducing the bounding sphere concept. Division based technique to calculate the volume, centroid and moment of inertia of a polyhedral particle is discussed.Secondly, using the geometric topology of vertices, edges and faces of polyhedral particles and the geometric characteristics of spherical particles, contact algorithms are developed for collision between three-dimensional spherical particles, polyhedral particles, and the surrounding environment. The algorithm determined the contact force by finding the penetration, the locations and relative velocities of the contact. Finally, a DEM program is developed, which contains the proposed particle generation algorithm and contact algorithm. Several accumulation problems of free falling spherical particles, polyhedral particles and the complicated shape particles in a quadrate box are simulated toshown the validity of the algorithms.