Self-Contact of Rods via Unconstrained Energy Minimization Technique

The objective of this project is to use numerical optimization methods to investigate the feasibility of obtaining self-contact solutions for inextensible, shearable, and isotropic thin rods via numerical continuation of a twist parameter applied at one end and a static potential along the rod. A semi-circular boundary condition is considered as a common example which can readily produce contact phenomena. We impose an energy potential of the form e--kx /x as presented in [1], that will prevent self-penetration of the elastic rod. Using these techniques, we observe the emergence of multiple contact points dependent upon the applied twist.