The compaction of aggregates of non-spherical viscoplastic particles

Abstract

This dissertation presents a study of the compaction of aggregates of non-spherical, viscoplastic particles under external load. A numerical model is developed in which each particle is treated individually, including the appropriate constitutive equations, kinematic conditions, and contact constraints, for every particle in the aggregate. The advantage of the model is that it can be applied to aggregates of particles that have a wide range of shape, size and properties.

A penalty iterative method has been derived to improve the efficiency of computing. Substitution of the proper value of the bulk modulus reduces the time of convergence and speeds up calculation. Also, the use of a sparse matrix approach saves a large amount of computer memory and increases the capability of the technique to handle large numbers of particles. A mesh update algorithm was generated based on a system of mixed triangular and quadrilateral elements. The algorithm is used to detect contact, generate meshes, modify concave elements and prevent locking. A general triangular mesh system is used to solve all problems at the same time, but the number of triangular elements need to be appropriately controlled due to their lower number of degrees of freedom. A series of numerical simulations for both single and multiple materials are presented to demonstrate the efficiency and accuracy of the model, and to visualize the process of compaction. The number of particles in these simulations ranges from tens to thousands. This work presents the first viscoplastic simulation model using the discrete element method applied to non-spherical particles.

This model has been used to study the effects of particle size, shape, distribution, orientation, mechanical properties, and compaction. As expected, larger numbers of granular elements yield more precise solutions. However, the detailed behavior of a single element can have considerable effect on the response of the whole system. Several factors have significant impact on the behavior of granular systems including void ratio, void shape, distance between voids, and void pattern. The algorithms presented here are useful for a wide variety of problems involving granular media that can be characterized as visco plastic in this behavior. The results presented here provide significant insight into the fundamental behavior of granular media under compaction conditions, including prediction of the overall aggregate stress-strain response.