Self-contact for rods on cylinders

TL;DR

This paper analyzes self-contact phenomena in elastic rods constrained on cylinders, providing a simplified variational framework and characterizing the structure of minimizers with a focus on the continuity of contact points.

Contribution

It introduces a novel variational approach for rods on cylinders and fully characterizes the structure of constrained minimizers with a new continuity result.

Findings

The set of self-contact points is continuous.

The variational setting simplifies the analysis of self-contact.

Complete characterization of minimizers in the constrained problem.

Abstract

We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a second-order functional of a single scalar variable, and the self-contact constraint is written as an integral inequality. Using techniques from ode theory (comparison principles) and variational calculus (cut-and-paste arguments) we fully characterize the structure of constrained minimizers. An important auxiliary result states that the set of self-contact points is continuous, a result that contrasts with known examples from contact problems in free rods.