Partial constraint singularities in elastic rods

TL;DR

This paper develops a unified classical framework for analyzing partially constrained elastic rods, addressing singularities in shape and reactions, and applicable to various contact and adhesion problems.

Contribution

It introduces a comprehensive approach that unifies sleeve and adhesion problems, providing clear derivations and linking reaction forces to energy balance and material momentum.

Findings

Unified treatment of sleeve and adhesion problems

Derivation of reaction forces from energy balance

Applicable to diverse contact and locomotion scenarios

Abstract

We present a unified classical treatment of partially constrained elastic rods. Partial constraints often entail singularities in both shapes and reactions. Our approach encompasses both sleeve and adhesion problems, and provides simple and unambiguous derivations of counterintuitive results in the literature. Relationships between reaction forces and moments, geometry, and adhesion energies follow from the balance of energy during quasistatic motion. We also relate our approach to the balance of material momentum and the concept of a driving traction. The theory is generalizable and can be applied to a wide array of contact, adhesion, gripping, and locomotion problems.