Buckling of knitted fabric wrapped around a rigid cylinder

Knitted fabrics exhibit high flexibility due to their periodic loop structures formed by bent yarns. Under compressive loading, they develop three-dimensional (3D) wrinkling patterns that reflect nonlinear interactions between yarn elasticity and local loop deformations, as observed when the sleeves of a sweater are rolled up. Despite their widespread use in garments and medical textiles, the relationship between loop-level geometry and macroscopic buckling remains less understood. Here, we investigate the 3D deformation of knitted fabrics wrapped around a rigid cylinder under uniaxial compression. Circumferential and axial stitch numbers are systematically varied to determine how loop geometry affects the evolution of wrinkle patterns. Samples with a small number of circumferential stitches exhibit sequential wrinkle formation from the compressed end, leading to an accordion-like wrinkle pattern, whereas those with a larger number of stitches form helical wrinkles simultaneously across the surface. Wrinkle morphology changes progressively with stitch geometry, accompanied by systematic variations in compressive force, loop deformation, and helical wrinkle angle. The development of helical wrinkles originates from subtle structural asymmetries introduced during manufacturing processes, including the tension applied during knitting and the direction of sample assembly. These results demonstrate that small variations in local loop deformation can lead to substantial differences in wrinkle morphology, highlighting the sensitivity of macroscopic buckling to microscopic structural features. The study establishes a direct link between loop-level mechanics and global deformation behavior, providing a basis for the predictive design of knitted structures with tailored mechanical responses and complex 3D patterns.

💡 Research Summary

This paper investigates the three‑dimensional buckling behavior of plain‑knit fabric tubes wrapped around a rigid cylinder when subjected to axial compression. By systematically varying the number of stitches in the circumferential (wale) direction (Nw = 40–60) and the axial (course) direction (Nc/Nw = 0.5–2.0), the authors explore how loop‑level geometry controls the onset and evolution of surface instabilities.

Fabrication was performed on a digital V‑bed knitting machine using 100 % cotton yarn, with a fixed stitch size (parameter = 6) and consistent roller‑advance settings to control yarn tension. After knitting, each tube was placed on a 70 mm‑diameter steel cylinder and compressed up to 30 % of its natural length at 5 mm s⁻¹. Force–displacement data were recorded, and high‑speed front‑view video captured the wrinkle formation. Image‑processing extracted wrinkle wavelength, angle, pitch, and the deformation of individual Ω‑shaped loops (horizontal spacing w and vertical spacing c).

Force–displacement curves show an initial steep rise followed by a gradual increase; the point where the steep rise first appears is defined as the peak force (Fpeak), representing the critical buckling load. Fpeak increases markedly as Nw decreases (tighter wrapping) and as the aspect ratio Nc/Nw grows, indicating that tighter circumferential confinement and larger axial stitch counts enhance yarn‑yarn contact, friction, and loop bending, thereby stiffening the structure.

Two distinct wrinkle modes emerge. When Nw is small (tight wrapping), wrinkles appear sequentially from the loaded edge, forming vertical, ring‑like undulations orthogonal to the compression direction. The spacing of these wrinkles matches the loop width, and their propagation speed scales with the compression rate. Conversely, for larger Nw (looser wrapping) and higher Nc/Nw, a helical (single‑sided, counter‑clockwise) wrinkle pattern develops almost simultaneously across the entire surface. The helical pitch and angle increase roughly linearly with Nc/Nw, and the onset of this mode occurs near the maximum imposed strain (≈30 %).

A key finding is that the helical mode is seeded by subtle manufacturing asymmetries. Variations in roller‑advance tension and knitting direction leave a residual torque in the fabric, biasing loop geometry toward a slight Ω‑asymmetry. This pre‑existing bias causes non‑uniform shear during compression, steering the whole tube into a helical deformation. Experiments confirm that altering the roller‑advance setting reverses the rotation direction of the helical wrinkles, underscoring the sensitivity of macroscopic buckling to microscopic loop asymmetry.

Loop‑scale analysis shows that before buckling, individual loops undergo significant changes in w and c; larger reductions in w (horizontal compression) and increases in c (vertical stretch) correlate strongly with higher Fpeak values. The nonlinear increase in loop curvature amplifies contact area and friction, which dominate the mechanical response beyond simple elastic bending.

The authors conclude that (i) the circumferential stitch count and the axial‑to‑circumferential stitch ratio are primary design parameters governing whether a knit tube exhibits sequential vertical wrinkles or global helical buckling; (ii) residual torque from the knitting process is a deterministic source of helicity; and (iii) loop‑level bending and friction constitute the dominant nonlinear mechanisms that must be incorporated into predictive models.

These insights provide a practical design framework for engineered textiles where controlled 3‑D morphologies are desired—such as compression garments, medical wraps, wearable robotics, and morphable soft structures. The work also highlights the need for multiscale modeling approaches that capture discrete loop interactions, friction, and geometric nonlinearity, moving beyond traditional continuum buckling theories.