MechE PhD Prospectus Defense: Amani Campbell

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

ABSTRACT: ibers 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 infor-mation as pulses of light. As slender structures, fibers are susceptible to distinctive deformations such as bending, buckling, and stretching. However, their collective behavior, particularly when they entangle with one another or interact within other systems, remains less well understood. When integrated into granular assemblies, fibers impose geometric constraints that fundamentally alter the bulk mechanical re-sponse, producing load-bearing behaviors reminiscent of engineered metamaterials. Conversely, 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. Combining an elastic material, such as string, with granular matter, such as rocks, can yield stable, load-bearing, free-standing 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. By extending the applied load range from 500 N, as in our previous work, to 40 kN, we explore the mechanical response of these columns under extreme uniaxial compression. We find that strategic winding of 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 like-lihood 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 ca-bles, 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 me-chanical 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 gives rise to a plethora of dynamic behav-iors, including the emergence of a distinct traveling knot.

COMMITTEE: ADVISOR/CHAIR Professor Douglas Holmes, ME/MSE; Professor Abigail Plummer, ME/MSE; Professor James Bird, ME/MSE; Professor Ousmane Kodio (UCSB)