Date of Award

5-11-2025

Date Published

June 2025

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Physics

Advisor(s)

Joseph Paulsen

Subject Categories

Physical Sciences and Mathematics | Physics

Abstract

Nature provides many examples of thin sheets and shells, from flower petals to graphene sheets. Such materials can exhibit complex deformations such as creases, folds and wrinkles, particularly in thin, flexible structures like cylindrical shells and ribbons. Here we investigate the geometric transformation and mechanical response of a twisted thin tube, which is made from a thin polymer sheet. In Chapter 2, an interesting "locking behavior" was found in a thin cylindrical shell. After an initial compression, the shell can be twisted with little resistance until it reaches a “locking angle”, which coincides with the appearance of an ordered wrinkle pattern. We construct a simple geometric model to predict the morphology of the shell and the locking angle under different compression. We also perform “force-controlled” experiments by applying a small tension to the shell as well as twisting it in the Rheometer, in excellent agreement with our model. Our results establish a route to a tunable locking material—a system with an interval where it is freely deformable, and where the endpoints of this interval can be changed continuously over a wide range. Chapter 3 shows how the boundary conditions affect the geometric structures of a twisted cylinder and how "pre-creasing" alters the behavior of a twisted crimped tube. By applying two creases to the tube prior to twist, we observe the formation of an ordered structure composed of repeating triangular facets oriented at varying angles. We then measure the exerted torque during the twist and analyze how the structural evolution depends on parameters such as material thickness and the twist angle. Our findings show that, similar to twisted ribbons, pre-creased toothpaste tubes exhibit a approximately linear increase in torque and, under certain conditions, develop a creased helicoid structure. Furthermore, we explore how the length of pre-creases influences the extent of triangular facet region as the twist angle increases. This study provides insights into controlling the buckling of thin shells, offering a potential pathway for designing ordered structures in soft materials. In Chapter 4, we consider another promising research direction in this system. By measuring the normal force exerted on a cylindrical shell subjected to cyclic compressions, we investigate the mechanical response of a thin crumpled shell under different loading protocols, revealing memory effects in crumpled sheets. In addition to the force-verses-compression measurements, we analyze acoustic signals and images captured during the experiment to track the evolution of folds and ridges, providing other ways of observing memory formation. Our findings highlight intriguing memory effects in a cylindrical sheet under cyclic compression or twist, contributing to a deeper understanding of memory in materials. Our study highlights the rich mechanical behaviors that emerge in thin cylindrical shells under twisting and compression, from locking transitions to ordered facet formation and memory effects. By combining experimental observations with theoretical modeling, we provide new insights into how geometric and mechanical constraints govern ordered patterns in thin sheets. These findings not only advance our understanding of buckling patterns and memory formation in soft materials but also suggest potential applications in designing tunable metamaterials.

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