Buckling of knitted fabric wrapped around a rigid cylinder

TL;DR

The paper addresses how loop-scale geometry in plain knitted fabrics governs macroscopic buckling when wrapped around a rigid cylinder and compressed axially. By systematically varying walewise $N_w$ and axial $N_c$ and performing force–displacement tests, loop-deformation tracking, and wrinkle analysis, the authors identify two distinct buckling regimes: tightly wrapped knits produce sequential, accordion-like rings, while looser wraps form nearly synchronous helical wrinkles with the average pitch angle $ar{\theta}$ increasing with compression. They link macro behavior to microscopic loop kinematics via measurements of wale length $w$, course length $c$, and the loop aspect ratio $c/w$, and demonstrate chirality origins through knitting-direction reversal and pre-twisting experiments, affecting $F_{\rm peak}$. Overall, the work establishes a direct loop-scale to macro-buckling connection, enabling predictive design of knitted textiles with programmable 3D morphologies and potential soft-actuation applications, and suggests future numerical modeling to further quantify yarn-scale mechanics and frictional contacts.

Abstract

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.

Figures (5)

• Figure 1: Snapshots of the compression process for knitted samples wrapped around a rigid cylinder. The sets of walewise (circumferential) and coursewise (axial) knitting numbers, $(N_w, N_c)$, are (a) (40, 80), (b) (50, 100) and (c) (60, 120). Each sample is compressed to 30% of its natural length $L_0$ using an acrylic plate mounted on the force-testing machine. Snapshots of compression levels of 0%, 20%, 50%, and 70% are shown here. We apply a displacement, $\Delta$, to measure the compression force, $F$, and analyze wrinkles on the knit surface.
• Figure 2: (a) Force–strain curves for samples for several sets of knitting numbers, $(N_w, N_c)$. We classify the color of the curves based on the aspect ratio, $N_c/N_w$, and tightness, $N_w$; $N_c/N_w = 0.5, 1.0, 1.5$ and $2.0$ as green, blue, yellow, and magenta, respectively. Each darker color represents the result for a larger $N_w$. A representative peak force $F_{\rm peak}$ is highlighted by a filled circle on the curve. (b) Relationship between the peak force $F_{\rm peak}$ obtained from the force–strain curves in (a) and the aspect ratio, $N_c⁄N_w$.
• Figure 3: Characteristic length scales of the unit loop. (a) The inset illustrates the initial $(w_0, c_0)$ and compressed $(w, c)$ wale and course lengths, and the plot shows $c$ and $w$ as functions of axial displacement $\Delta$ for a representative sample with $(N_w, N_c) = (40, 80)$. (b) The change of the aspect ratio of the loop, $c/w$ upon compression up to the buckling ($F\lesssim F_{\rm peak}$) for $(N_w, N_c) = (40, 80), (50, 100), (60, 120)$. (c) The ratio of the initial wale and course lengths, $c_0/w_0$, against the aspect ratio of the knitting number, $N_c/N_w$. (d) (Linear) Decrease ratio of $c/w$ upon axial compression, $\alpha$, plotted as a function of $N_c/N_w$ (See definition of $\alpha$ in (b)).
• Figure 4: Helical buckling of cylindrical knits. (a) Typical example of image analysis used to extract wrinkle patterns and to define the pitch angle $\theta$ during compression of the knitted sample ($(N_w, N_c) = (60, 120)$). The extracted wrinkles approximated by sinusoidal curves are superimposed on the original images. The pitch angle for each wrinkle, $\theta$, is obtained from the tangent of the center of the corresponding sinusoidal curve. (b) Variation of the average pitch angle $\bar{\theta}$ with the imposed displacement $\Delta$ for samples with $N_w = 60$. The average pitch angle, $\bar{\theta}$, is obtained by taking the average of $\theta$ over all wrinkles for a given $\Delta$ and the shaded regions represent the error bar.
• Figure 5: Roles of intrinsic (natural) twist of cylindrical knits. (a) The force responses of the sample with the same knitting numbers, $(N_w, N_c) = (60, 120)$, manufactured in the different knitting order. We plot the force displacement curve of the sample obtained through the knitting processes (right$\to$left) illustrated in the main text as a green curve (replotted from Fig. \ref{['fig:2']}(a)). The orange curve represents the force response of the sample with the opposite knitting order. The snapshots of $\Delta/L_0 = 0.40$ are shown in the inset. (b) Force displacement curves of pre-twisted cylindrical knits $(N_w, N_c) = (40, 80)$. We compare the force-response of the knit pre-twisted by $\pm180^{\circ}$ (ccw, cw, respectively) with the twistless sample (denoted as ref). The result of the twistless case is replotted from Fig. \ref{['fig:2']}.