MechE PhD Final Oral Defense: Amani Campbell

TITLE: THE MECHANICS OF DFIBER CONFINEMENT AND SELF-ENTANGLEMENT FROM ELASTOGRANULAR COLUMNS TO KNOTTING IN CURVED RODS

ABSTRACT: Fibers are ubiquitous in both natural and engineered systems, from fibrous root networks that stabilize soil and wool textiles that help to regulate body temperature to thin strands of glass or plastic fibers used in fiber optic cables to transmit information as pulses of light. Because fibers are thin structures, they are susceptible to deformations such as bending, buckling, and stretching. Their collective behavior, however, particularly when they entangle with one another or interact within other systems, remains less well understood. Fibers impose geometric constraints when integrated into granular assemblies that fundamentally alter the bulk mechanical response, producing load-bearing behaviors reminiscent of engineered metamaterials. Additionally, when considered in isolation, fibers, and especially those with intrinsic curvature, exhibit complex self-entangling dynamics that remain poorly understood, despite their relevance to natural and synthetic systems alike. By examining fibers in these two distinct yet complementary contexts, this thesis provides new insight into fiber geometry and interactions, and how they govern stability and strength. While this work focuses heavily on the fundamentals of granular jamming, jamming itself is not restricted to granular matter. Studies have extensively explored granular, laminar (layer), and, to a lesser extent, fiber jamming to achieve variable stiffness. Grains can be considered 0D structures, with no dimension significantly different from the other. Layers (sheets, plates, etc.) are 2D structures, where two dimensions are significantly larger than the other. Fibers are 1D structures, where one dimension is significantly larger than the other two. What happens when one system incorporates two of these jamming mechanisms? Combining an elastic fiber, such as a string, with granular matter, such as rocks, can yield stable, load-bearing, freestanding elastogranular structures. The simplest example, an elastogranular column, is formed by confining grains with loops of fiber. In this thesis, we demonstrate that we can significantly enhance the stiffness and load-carrying capacity of the columns by incorporating high-strength elastic fibers, such as braided Dyneema® (UHMWPE) and twisted Kevlar® rope. We extended the applied load range from 500 N, as in our previous work, to 40 kN, to explore the mechanical response of these columns under extreme uniaxial compression. We find that strategically winding the fibers around the column perimeter, at specific grain-to-fiber ratios (ψ), leads to a substantial increase in stiffness. Furthermore, introducing a controlled preloading condition consistently amplifies stiffness, an effect we attribute to the intrinsic strain-hardening behavior of the fibers under large mechanical loads. The second part of this thesis focuses on fiber entanglement through self-knotting. Prior studies of knots in slender structures have focused either on the statistical likelihood of knot formation in vibrated granular chains and strings or on the topological mechanics of knots in elastic rods. Knots are ubiquitous, appearing in electronic cables, DNA molecules, long-chain polymers, and even in hair, where they often prove unavoidable. In particular, trichonodosis, the spontaneous knotting of hair fibers along the shaft, is especially prevalent in tightly curled and coiled hair. Motivated by this biological phenomenon, we design physical rod experiments to establish a mechanical parallel and systematically study self-knotting under controlled mechanical agitation. These experiments reveal that increasing rod curvature not only increases the probability of knot formation but also the likelihood of a plethora of dynamic behaviors, especially a distinct traveling knot.

COMMITTEE: ADVISOR Professor Douglas Holmes, ME/MSE; CHAIR Professor Joerg Werner, ME/MSE; Professor Abigail Plummer, ME/MSE; Professor Jacy Bird, ME/MSE; Professor Ousmane Kodio, ME/MSE