On April 10, 2020 Kyle VanderWerf successfully defended his thesis: “Geometry and Contact Mechanics of Athermal Jammed Packings of Frictionless Spherical and Nonspherical Particles” (Advisor: Corey O’Hern).
VanderWerf explained ”The jamming transition in granular packings is one of the most important systemic phenomena discovered in the field of granular physics in the past 30 years. I model jammed systems by writing computer simulations to generate large ensembles of jammed packings in order to carry out statistical studies of the geometry of these packings’ networks of interparticle contacts.
My work is divided into two major areas of focus. In the first half of my research, I study jammed packings of nonspherical particles in 2D and 3D. I explain the apparent deficiency in the number of contacts these packings possess using differential geometric arguments in the hyperdimensional configuration space of the constituent particles’ degrees of freedom, and identify key shape parameters that determine these packings’ geometric properties. In the second half of my research, I study the mechanical response of jammed packings of disks to deformation. I show that the pressure scaling of the shear modulus of these packings is dependent on configurational rearrangements that occur with compression, and establish a deep link between the ability of a cyclically-compressed disk packing to be trained into a reversible state, and the occurrence of plastic events in the system during compression.”
VanderWerf is still deciding what to do post degree.
Thesis abstract: I perform computational studies of quasistatically jammed packings of frictionless particles of a variety of shapes. Each of the four studies presented in this dissertation focuses primarily on the connection between the mechanical and geometric properties of these packings – specifically, how physical aspects such as force and torque balance, pressure, and shear and bulk moduli correlate with (a) constituent particle shape, (b) the degree of particle ordering in packings, and (c) the packings’ networks of interparticle contacts. I also investigate how each of these geometric properties affect each other. For example, in the first study, I examine the relationship between constituent particle shape, packing fraction, and contact number, and demonstrate a variety of correlations between these properties for two-dimensional jammed packings of nonspherical particles. In the second study, this analysis is extended to three dimensions, where an additional shape parameter is necessary to describe the packing fraction at jamming onset, and the effect of orientational ordering is considered. In the third study, I show that the scaling exponents of the ensemble-averaged shear modulus of jammed disk packings as a function of pressure are dependent on changes in the contact network that occur as the pressure increases, and demonstrate that jammed packings can unjam via isotropic compression. Finally, in the fourth study, I present the preliminary results of research into cyclically-compressed jammed disk packings, which are able to be trained into reversible states over time if the amplitude of the compression is sufficiently small, but which remain irreversible indefinitely if the amplitude of the compression is too large.