Knitting Multistability

TL;DR

This work demonstrates that weft-knitted textiles can realize curved, multistable surfaces by embedding perpendicular residual stresses that mimic a pre-stressed bilayer. By designing unit-cell stitch patterns (Step, Windmill, H-shaped) and tuning pattern geometry, yarn type, and machine parameters, the authors achieve controlled snap-through transitions and multiple stable configurations, validated by finite-element simulations using orthogonal thermal-expansion mismatches. Functionality is added by integrating conductive yarn to create textile switches with built-in haptic feedback, enabling soft, motor-free wearables and interactive lighting. The approach offers scalable, breathable, and programmable soft devices for wearables, safety gear, and home textiles, with potential extensions to broader knit patterns and yarn-scale analyses.

Abstract

Curved elastic shells can be fabricated through molding or by harnessing residual stresses. These shells often exhibit snap-through behavior and multistability when loaded. We present a unique way of fabricating curved elastic shells that exhibit multistability and snap-through behavior, weft-knitting. The knitting process introduces internal stresses into the textile sheet, which leads to complex 3D curvatures. We explore the relationship between the geometry and the mechanical response, identifying a parameter space where the textiles are multistable. We harness the snapping behavior and shape change through multistability to design soft conductive switches with built-in haptic feedback, and incorporate these textile switches into wearable devices. This work will allow us to harness the nonlinear mechanical behavior of textiles to create functional, soft, and seamless wearable devices. This includes but is not limited to the devices for additional cycling visibility and safety that we envision.

Figures (35)

• Figure 1: Knitting on the front and back bed of a knitting machine allows us to create corrugated textiles. A) The Kniterate machine. B) Needles are arranged in two parallel beds facing each other. Colored yarns are held together in needles, but offset to color the two faces of the fabric in orange and blue. This needle configuration shows the rib structure in H. C) A knit sample is approximated as a bilayer with perpendicular internal stresses. D) A high aspect ratio sample is cut in the warp direction. A schematic shows the dominant curvature. E) A high aspect ratio sample is cut in the weft direction, resulting in an opposing dominant curvature. F) On the face of the fabric the yarns lie parallel to the warp direction, illustrated with a macro photograph with corresponding schematic. G) On the reverse side the fabric yarns are parallel to the weft direction, shown via imaging and associated schematic. H) Corrugations in the weft direction are known as a rib fabric. We visualize these corrugations by imaging the cross-section. This fabric is much more compliant in the weft direction as the vertical corrugations unfold. I) Corrugations in the warp direction are known as a garter or links-links fabric. A cross-section image depicts the shape of the corrugations. In a tensile test, these corrugations cause this fabric to be compliant in the warp direction but stiff in the weft direction. All samples are knit on the Kniterate machine.
• Figure 2: By altering the unit cell knitting patterns we can tune both the final shape and mechanical response of the textile. A) The Step pattern unit cell and corresponding knit sample. B) The Windmill pattern unit cell and corresponding knit sample. C) The H-shaped pattern and corresponding knit sample. D) A Step sample (i) before loading, (ii) during loading, and (iii) after unloading. E) A Windmill sample (i) before loading, (ii) during loading, and (iii) after unloading. F) An H-shaped sample (i) before loading, (ii) during loading, and (iii) after unloading. G-I) Force-displacement measurements for (G) the Step sample, (H) the Windmill sample, and (I) the H-shaped sample, with force drops marked and the region of negative force highlighted by a gray horizontal line. All samples are knit on the Kniterate machine.
• Figure 3: Finite Element simulations demonstrate that the internal stresses in our knits resemble those of a perpendicularly pre-stressed bilayer. A) Thermal expansion induces curvature and internal stresses in a bi-layer shell with mismatched orthogonal coefficients of thermal expansion. B) This simplified representation of the fabrics is sufficient to achieve the curved configurations observed in experiments. C) When a localized displacement is applied to the boundaries of the model, snapping into a second stable configuration is observed. D) Numerically predicted evolution of the strain energy as a function of applied displacement exhibits two minima—one at zero displacement and another at a finite, nonzero displacement—confirming multistability.
• Figure 4: A) Microscope images of each of the yarns used. B) Tensile tests of the yarns. C) Images of the samples knit from alternate yarns D) Tensile tests of the 'H-shape' knit pattern, knit with different yarns. E) Photographs of samples knit with two elastomeric yarns on the Shima Seiki SWG machine in different stitch sizes F) Tensile tests of the 'H-shape' knit pattern with different stitch sizes. G) Repeated tensile tests of the sample from Figure \ref{['fig:diff-geometries']}C, knit with four ends of elastomeric yarn on the Kniterate machine.
• Figure 5: As the geometric parameters of a single unit cell vary, so do the mechanical properties and 3D shapes of the textile. A) Three parameters define our H-shaped unit cell ($n_a,n_b,$ and $n_d$). Units of each parameter are number of stitches. B) All three parameters are varied and the force-displacement response measured. Multistable samples are highlighted in purple, while monostable samples are color-coded based on the dominating folds in their stable configuration: yellow for the ‘rib’ configuration and green for the ‘garter’ configuration. C) Snapshots of samples with (i) $n_a$ = 4, $n_b$ = 12, and $n_d$= 12. (ii) $n_a$ = 4, $n_b$ = 12, and $n_d$= 8. (iii) $n_a$ = 4, $n_b$ = 12, and $n_d$= 4. Additional photos are shown in Figures \ref{['si_fig:d12 photos']}, \ref{['si_fig:d8 photos']}, and \ref{['si_fig:d4 photos']}. D) We visualize which samples are monostable rib -- yellow, -- monostable garter -- green, -- and bistable -- purple -- in the 3-D space of our parameters. All samples were knit on the Kniterate machine.