Piecewise linear constitutive relations for stretch-limited elastic strings

TL;DR

This paper introduces a new class of stretch-limiting constitutive relations for elastic strings, allowing stretch to be a bounded, piecewise linear function of tension, with explicit solutions for specific string configurations.

Contribution

It presents a novel stretch-limiting constitutive model for elastic strings, extending traditional elasticity theories with explicit solutions for certain motions.

Findings

Stretch is modeled as a bounded, piecewise linear function of tension.

Explicit solutions derived for catenaries and piecewise constant stretched motions.

The model extends classical elasticity to include stretch-limiting behavior.

Abstract

This study proposes a simple and novel class of stretch-limiting constitutive relations for perfectly flexible elastic strings drawing from modern advances in constitutive theory for elastic bodies. We investigate strings governed by constitutive relations where stretch is a bounded, piecewise linear function of tension, extending beyond the traditional Cauchy elasticity framework. Our analysis includes explicit solutions for both catenaries and longitudinal, piecewise constant stretched motions.