Loop Formation and Contact Problems in Elastic Rods

This thesis examines two problems involving the equilibrium configurations of intrinsically straight and intrinsically curved, long elastic rods. In both cases the rod is in a planar configuration and is clamped at one end and has a load applied at its free end. The first problem concerns intrinsically curved rods, which undergo very large deformations such that they may be pulled nearly straight, or may form a loop, or are bent in such a way that their curvature is of the opposite sign to their intrinsic curvature. Using a combination of experiments, numerical simulations and analysis, the aforementioned configurations are considered from a global qualitative perspective. The thesis gives the critical conditions for loop formation and critical points at which a rod may jump from one configuration to another. The second problem examines the equilibrium configurations of an intrinsically straight rod that is pressed against an inclined wall. The critical point at which tip contact changes to line contact is given, where we again find excellent correlation between experiments, numerics and analysis. Overall, the thesis contributes to our understanding of the mechanics of rods with applications in a variety of real world scenarios - from structural design, to cable laying problems, and the mechanics of animal vibrissae.