Uniform boundary conditions on models of spherical particles through alpha shape surface tracking and Laguerre-Voronoi diagrams

This study describes the adaptation of the alpha-shape three-dimensional surface reconstruction technique to boundaries of spherical particle packings, such as those modeled using Discrete Elements. The alpha shape technique is employed to reconstruct a boundary surface for a packing as well as to assemble a Laguerre-Voronoi Diagram of the packing's boundary. The reconstructed surface can be used to track the evolution of the packing surface, while the surface diagram can be used to directly obtain the discrete force vectors that result from applying a uniform stress tensor (Static Uniform Boundary Condition), as well as the discrete velocity vectors that result from applying a uniform velocity gradient tensor (Kinematic Uniform Boundary Condition) to a model of spherical discrete particles. Doing so continuously throughout a simulation allows for the application of uniform boundary conditions on spherical discrete particles, whilst enabling precise tracking of stress and deformation tensors of the packing. An implementation of this novel approach in the Yade open-source DEM code is detailed here. The power and versatility of the real-time boundary tracking approach is demonstrated using some boundary value problem simulations on polydisperse spherical particle models.