Piecewise linear constitutive relations for stretch-limited elastic strings.

This article introduces a novel class of stretch-limiting constitutive relations for perfectly flexible elastic strings, where the stretch is modeled as a bounded, piecewise linear function of tension, differing from classical Cauchy elasticity that expresses tension explicitly as a function of stretch. The proposed model incorporates distinct tangent moduli for extension and compression and imposes physical limits on maximum stretch and compression, capturing behaviors unattainable by traditional constitutive theories. Explicit solutions are derived for static catenaries under gravity and for dynamic motions with piecewise constant stretch, illustrating key differences from previous models and offering potential applications in civil engineering and biological systems. The work provides a foundational framework for further analytical and numerical studies of stretch-limited strings in various physical contexts.