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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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Longitudinal shock waves in a class of semi-infinite stretch-limited elastic strings
In this paper, we initiate the study of wave propagation in a recently proposed mathematical model for stretch-limited elastic strings. We consider the longitudinal motion of a simple class of uniform, semi-infinite, stretch-limited strings under no external force with finite end held fixed and prescribed tension at the infinite end. We study a class of motions such that the string has one inextensible segment, where the local stretch is maximized, and one extensible segment. The equations of motion reduce to a simple and novel shock front problem in one spatial variable for which we prove existence and uniqueness of local-in-time solutions for appropriate initial data. We then prove the orbital asymptotic stability of an explicit two-parameter family of piece-wise constant stretched motions. If the prescribed tension at the infinite end is increasing in time, our results provide an open set of initial data launching motions resulting in the string becoming fully inextensible and tension blowing up in finite time.
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- Award ID(s):
- 1703180
- PAR ID:
- 10377820
- Date Published:
- Journal Name:
- Mathematics and Mechanics of Solids
- Volume:
- 27
- Issue:
- 3
- ISSN:
- 1081-2865
- Page Range / eLocation ID:
- 474 to 490
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1177/10812865211025582
