On stretch-limited elastic strings

Abstract

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.

Longitudinal shock waves in a class of semi-infinite stretch-limited elastic strings

“…Longitudinal motion for stretch-limited elastic strings. In this paper we study the dynamics of a simple class of uniform, semi-infinite stretch-limited elastic strings introduced in [14]. The constitutive relation can be expressed via (2.3) but not via (2.2), and we assume that the string becomes inextensible once a threshold value of tensile force is reached.…”

“…In [14], we initiated the study of these generalized relations for strings by considering a class of stretch-limited elastic strings. For these strings, the stretch is an explicit function of the tension of the string, but not vice versa, and the stretch is constrained between two limiting values.…”

“…These properties are incapable of being modeled within the standard framework for elastic strings. In [14] we studied stationary configurations of finite stretch-limited strings suspended between two points under the force of gravity (catenaries) containing both inextensible segments (where the stretch is maximized) and extensible segments.…”

On an elastic strain-limiting special Cosserat rod model

“…• elastic strings [48,49]. However, this paper is the first work studying a set of strain-limiting constitutive relations for special Cosserat rods.…”

“…Thus, such bodies must be described either by relations such as (1.3) or even the more general class (1.2), with these relations not being invertible. Recently, Rodriguez studied such stretch-limiting constitutive relations for elastic strings in both static [48] and dynamic [49] settings, and Rajagopal and Rodriguez studied certain inelastic behavior for the quasistatic motion of an inextensible, unshearable, viscoelastic rod [45].…”