Large deformation mechanics of loop pile structure under compression loading modelled as buckled elastic rod

Abstract

Loop pile fabrics play a central role in technical textiles where compression resistance governs performance, yet no closed-form model has been available to predict their large deformation behavior. This study introduces an analytical framework based on Euler’s elastica theory, treating loop piles as buckled elastic rods subjected to compression. Explicit equations were derived to calculate the final maximum height (hf), maximum width (wf), and aspect ratio (AR), incorporating rod geometry and material properties. The model was validated through systematic compression tests on five recycled rubber rods with varying diameters and initial configurations. Results revealed excellent agreement between theoretical predictions and experimental measurements, with strong correlations (R = 0.967 for hf, R = 0.889 for wf, and R = 0.771 for AR) and acceptable error margins(hf ≤ 18.52%, wf ≤ 30.94%, and AR ≤ 21.38%). By combining rigorous theory with experimental validation, this work provides the first predictive tool for designing loop pile textiles, with direct applications in cushioning, geotextiles, and biomedical fabrics.