CAREER: Topological Assessment in Granular Materials

Haverford College, Haverford PA

Investigators

Abstract

Non-technical Abstract: Pouring a bucket of sand demonstrates the liquid-like potential of sand, yet beach-goers trust the same material to support their weight. Why do the beach-goers not sink into the sandy depths? Though we have the experience to understand that sands, powders, and other granular systems will flow like a fluid or support load like a rigid solid under certain conditions, nobody can reliably or precisely predict when, how, or why these systems will become rigid or flowing. This uncertainty is characteristic of a broad class of rigid, amorphous materials. Examples include sand as well as glass and plastics. Thus, by studying the origins of rigidity in granular materials, the principal investigator hopes to gain insight into a wide variety of systems. The focus of this project is the transmission of stress through the internal structure of a granular material is related to the bulk mechanical response of the material. The research team uses an imaging technique to measure the forces between particles throughout the material. The primary goal is to identify structures, not in the particles' spatial arrangement, but the patterns of force transmitted through the system. To understand these structures, the team leverages new methods to describe complicated networks and geometries. A secondary goal of the project is to manipulate these force-transmission structures to design materials with specific properties. The project will contribute to several educational goals, as well. Specifically, the principal investigator will provide training and mentorship to undergraduate and postdoctoral junior scientists involved in the research and integrate experimental techniques and ongoing research within the project's scope into the core physics curriculum. Additionally, the principal investigator will develop a workshop that prepares research mentors to train an effective population of junior scientists. Technical Abstract: The objective of this project is to understand the multi-scale origins of rigidity in amorphous granular materials. The research team will leverage photoelasticimetric imaging, a state of the art spatially- and force-resolved measurement technique, combined with high-resolution, composite imaging to characterize the structure and internal stress state of large granular packings in either biaxial compression or pure shear. The project's primary goal is to identify correlations between the bulk mechanical response of the material and the force-resolved measurements of the material's internal stress state. Prior observations suggest that structures at all scales contribute to the mechanical response of granular materials. Thus, both mean-field descriptions and particle-scale metrics are ill-suited to predicting material rigidity. In contrast, the principal investigator is developing a novel analytic approach based on algebraic topology and the science of networks, which identifies topological features that represent structures at all length-scales. To identify correlations between these topological features and the bulk material response, the research team uses the Support Vector Machines method. This machine learning technique has been effective in predicting local plasticity in colloidal glasses and wet, granular pillars. A secondary goal of the project is to develop strategies for materials design to reproducibly manufacture packings with prescribed topological properties in an approach reminiscent of the design of topologically insulating electronic materials. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.