Paper mechanics applied to cutting and flying

Paper is a commonplace material that many people encounter daily. Traditionally, paper has been a crucial medium for distributing information, from disseminating scientific breakthroughs to recording historical events. However, it has also been implemented in research to study the physics of thin sheets. In this thesis, we explore paper mechanics in the context of cutting and flying by studying the interaction between the sheet and a soft solid and a fluid, respectively.

First, we study how cutting mechanics are influenced when a flexible paper sheet replaces a rigid metal blade, stimulated by the observation that not all paper types are equally likely to give a paper cut. To study the interactions arising from the contact between a paper sheet and a soft solid, we attempted to cut into a tissue-mimicking gelatin slab at different cutting angles using paper blades with varying thicknesses. Three types of outcomes are observed: cutting, buckling, and indentation. Positioning the results in a phase diagram along with a model evaluating relevant competing stresses reveals why not all paper types are equally likely to cut: relatively thin sheets buckle before reaching the stress required for the initiation of a cut, while thick sheets predominantly only elastically deform the solid. The threshold for cutting is lowered when a slicing motion is added, making cutting possible for a larger range of paper thicknesses. Consequently, cutting with a paper blade is only permitted for certain combinations of paper thickness and cutting angles. The most hazardous thickness can be determined where the stress models for buckling and indentation intersect. We also show how the cutting ability of paper can be harnessed by implementing the most dangerous paper as a blade in a knife.

Second, we explore how different insect-inspired paper shapes settle through a fluid under gravity inspired by parachuting flight and co-existence of bristled and membranous wing shapes in miniature insects. To study the influence of insect morphology, we propose a lattice animal model to allow several distinct wing forms. Using an automated free-fall experiment to mimic parachuting flight, we explore the link between drag, shape, and area of these paper-insects. At intermediate Reynolds numbers, we find that large or compact shapes fall faster through the fluid, while sparse or small morphologies exhibit slower descent dynamics due to high drag. In an attempt to determine which lattice animals have the best performance in terms of both high and low drag at fixed area, we combine experiments and a genetic algorithm in a loop to search for high-performing shapes. Emerging shapes supported the initial finding that high drag is linked to sparse morphologies with long appendages. Conversely, shapes optimized for fast settling were compact. However, a distinct optimal form for either optimization remains unknown due to the non-reproducible paths of the emerging shapes. The rate of improved drag performance also depends on the direction of the evolutionary scheme, where the search for high-drag lattice animals is feasible within fewer generations than when pursuing lowdrag shapes. This reflects how competition between entropic effects and adaptive fitness limits whether a truly optimized form can be found.

In conclusion, implementing paper as an experimental medium has allowed us to explore complex dynamics associated with cutting and flying. The exploration of paper mechanics offers promising potential for future directions for research on both cutting with flexible sheets and settling paper shapes.