On stretch-limited elastic strings

TL;DR

This paper explores the equilibrium configurations of stretch-limited elastic strings, which cannot be compressed or extended beyond certain limits, revealing unique multiplicity and support configurations compared to classical elastic models.

Contribution

It introduces a novel class of stretch-limited elastic strings and analyzes their equilibrium states, including support positions and multiplicity, contrasting with classical elasticity models.

Findings

Support positions depend on stretch limits and support height.

Multiple equilibrium states can exist for stretch-limited strings.

Distinct behavior from classical elastic strings in equilibrium configurations.

Abstract

Motivated by the increased interest in modeling nondissipative materials by constitutive relations more general than those from Cauchy elasticity, we initiate the study of a class of stretch-limited elastic strings: the string cannot be compressed smaller than a certain length less than its natural length nor elongated larger than a certain length greater than its natural length. In particular, we consider equilibrium states for a string suspended between two points under the force of gravity (catenaries). We study the locations of the supports resulting in tensile states containing both extensible and inextensible segments in two situations: the degenerate case when the string is vertical and the nondegenerate case when the supports are at the same height. We then study the existence and multiplicity of equilibrium states in general with multiplicity differing markedly from strings satisfying classical constitutive relations.