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.

出于对通过本构关系比非柯西弹性模型更一般的本构关系建模非耗散材料的兴趣越来越高，我们开始研究一类受拉伸限制的弹性弦：字符串不能压缩得小于自然长度的一定长度，也不能拉长大于自然长度的一定长度。特别是，我们考虑了在重力（类别）的作用下悬挂在两点之间的弦的平衡状态。我们研究了在两种情况下导致拉伸状态同时包含可伸长段和不可伸长段的支撑位置：在弦垂直时的退化情况和在相同高度时的非退化情况。然后，我们研究平衡态的存在和多重性，其中，多重性与满足经典本构关系的弦明显不同。