| We develop a general computational model for a elastic rod which allows for extension and shear. The model, similar in mathematical construction to Cosserat rod theory, allows a wider variety of problems to be studied than previous models. In the first section we develop the continuous mathematical model, discretize the system to allow implementation on a computer, and then verify the model's output against classical buckling tests. We then develop a novel analytic solution for the critical buckling length of a vertically oriented, shearable elastic beam subject to gravity and show that the model's treatment of shear is correct. In the experimental section we analyze a number of different phenomena with the rod model. To begin, we explain the mechanical response of helically coiling tendrils. After self-collision is introduced, we explore the formation of plectonemes and solenoids in a highly extensible elastic string. We discuss a sheet adhering to a surface in several different regimes and use the rod model to discover a self-similarity solution in the low-damping limit. Physical entanglement is investigated in an experiment where randomly tumbled strings are used to derive scaling laws for the dynamics governing entanglement. Models for active internal forces and anisotropic surface friction are introduced to explain the mechanics of a newly observed mode of snake locomotion. Finally, we extend the model from a single filament to an arbitrary number of strings and begin exploration into behavior of cloth, ponytails, and combing hair. |
