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Motivated by the increased interest in modelling non-dissipative 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 non-degenerate 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.
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This content will become publicly available on April 14, 2026
Piecewise linear constitutive relations for stretch-limited elastic strings
Abstract This study proposes a simple and novel class of stretch-limiting constitutive relations for perfectly flexible elastic strings drawn 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 catenaries and longitudinal, piecewise constant stretched motions.
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- Award ID(s):
- 2307562
- PAR ID:
- 10613940
- Publisher / Repository:
- IMA_25
- Date Published:
- Journal Name:
- IMA Journal of Applied Mathematics
- Volume:
- 90
- Issue:
- 1
- ISSN:
- 0272-4960
- Page Range / eLocation ID:
- 99 to 114
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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