Analysis of disjoint two-dimensional and three-dimensional particle assemblies

This Dissertation contains the results of research on the development of a new discrete algorithm for analyzing the behavior of 2D and 3D assemblies of disjoint particles. The algorithm treats each particle as a 2D polygon, or as a 3D polyhedron, and generates contact normal and shear forces between two contacting particles when interference (overlap) occurs. The key new feature of the algorithm is a very efficient and effective multilevel contact detection scheme which makes it possible to treat the behavior of much larger assemblies of polygonal particles than has been possible in the past. The new logic scheme, which is in essence a dynamic boxing scheme, works equally well for 2D and 3D convex particles.; A computer program written in the C language has been prepared and executed to demonstrate the power of the new algorithm. Examples involving large assemblies of particles are presented to show the capabilities of the method for (a) analyzing quasi static assemblies of particles subjected to stress (such as soil or rock masses), and (b) investigating dynamic particulate flows (such as flows through hoppers and gates).; The algorithms is also intended to serve as a numerical basis for developing micro mechanical analyses of slip and failure processes in geologic materials (such as the dynamic growth of faults and failure bands) and for investigating the micro mechanics of fracture and fatigue of metals by tracking localized stress within the polycrystalline grain structure of the metal under quasi static load conditions. A number of additional tasks will have to be completed to make these types of analyses feasible, including the development of improved shear friction contact logic, and more elaborate tensile and compressive contact force logic.