  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.
