Constitutive Modeling of the Nonlinear Tensile Response of High-Strength Nanofiber Yarns Under Monotonic Loading

High-strength nanofiber yarns exhibit pronounced nonlinear tensile responses arising from their hierarchical fibrous architecture, yet compact constitutive descriptions remain limited. Here, high-strength polyacrylonitrile nanofiber yarns were prepared by post-drawing as-spun yarns above the glass transition temperature, and their aligned, stacked morphology was confirmed by scanning electron microscopy. Monotonic tensile tests at different loading rates were used to quantify the rate-dependent stress-strain response. The tangent modulus derived from the tensile curve varied strongly with strain, confirming clear deviation from linear viscoelasticity. To capture this behavior, two effective models were established: a modified nonlinear three-element model and a structural four-element model incorporating a nonlinear elastic contribution. Closed-form stress-strain expressions were derived for constant strain-rate loading and fitted to experimental data using nonlinear regression. Both models reproduced the measured tensile curves with high accuracy over the investigated loading-rate range, with correlation coefficients close to unity and low fitting errors. The identified parameters were highly consistent between formulations, indicating functional equivalence for the present monotonic tensile dataset. These results provide a compact framework for characterizing and designing hierarchical polymer nanofiber yarns.