Beaded metamaterials

Abstract

Beading transforms flexible fiber networks into load-bearing structures by incorporating rigid, discrete elements in programmable weave patterns. Beaded assemblies function as mechanical metamaterials, where emergent mechanical behaviors arise from the interplay between geometry and material properties. Here, we investigate how this interplay governs the global mechanics of bead-thread networks. Using a combination of experiment and simple modeling, we identify conditions under which beaded structures undergo superjamming - a mechanically locked state that dramatically enhances load capacity. Our results show how potentially limiting factors such as gravity and friction can be leveraged to extend the domain of soft materials design into applications that demand rigidity.

Fig. 1. Design and emergent stiffness of objects beaded using an angle weave technique.

a Sample angle-woven swatches comprised of adjoining loops of n beads, where n = 3–7. Non-Euclidean tiling of unit loops can lead to three-dimensional surfaces. Scale bars, 20 mm. b A beaded shell shown before tensioning (i), with thread pattern schematically traced over a photograph of otherwise opaque, 17 mm acrylic beads threaded with steel rope. Scale bar, 20 mm. Applying tension to the two free ends sends the half-dodecahedral shell out-of-plane (ii–iv). The structure becomes rigid across length scales by clamping the thread, capable of bearing large point (ii) and distributed (iii) loads. Scale bar, 100 mm. (iv), μ-CT reconstruction of the model of the same design using 10 mm acrylic beads (yellow) threaded with 0.25 mm nitinol wire (blue). Scale bar, 10 mm.

Fig. 2. A beaded shell is compressed between two plates.

a Photographs of the experiment. Constant tension (T₀) is applied to the thread ends as the indenter moves a distance δ. Shaded regions show the maximum and minimum force over all trials, and solid black lines show a moving average. Scale bar, 10 mm. b and c The force response (F) for identical shells threaded with different materials (0.25 mm diameter nitinol and 0.50 mm diameter nylon, respectively) as a function of δ, cycled three times across a range of T₀. Loading and unloading paths are marked with black and white arrows, respectively. d Maximum load as a function of tension for shells beaded with nitinol (blue) and nylon (green) thread. Maximum forces that occur in a superjammed regime are outlined. e Illustration of a 5-bead building block that comprises the model structure. Gray lines indicate bead hole orientation. f and g Tracking selected beads' motion over a single cycle across a range of T₀. f In-plane dilation of the bottom layer of beads measured by the length of exposed thread (Δϵ) as a function of δ. g Altitudinal angles θ₁ and θ₂ as a function of δ. h Projection of F as in-plane tension between two pink beads shown as a function of Δϵ. A 3-part piecewise linear fit is shaded behind each trial. The return path is not shown in (f–h). Source data is available in Supplementary Data 1.

Fig. 3. Decoupling (and recoupling) friction and geometry in beaded assemblies.

a Measuring friction in a planar ring of n = 4 beads. A sliding thread is pulled through a loop of constrained beads for a displacement δ. Constant tension (T₀) is applied to one end of the thread while tension (T) is read at the other for a range of T₀ and two thread materials. b Kinetic friction plateaus T^* plotted as a function of T₀ for planar bead rings where n ranges from 3 to 6. Dashed lines indicate linear fits of the data. c Dimensionless force (F/T₀) vs. indenter displacement (δ) for dilating planar bead rings using a spherical-tipped indenter with the same radius as a bead. Experiments for n = 3, 4, and 5 are shown as n-sided markers. Theory for n = 4 and zero friction is drawn in white, with blue and green lines showing a correction for bead-thread friction in nitinol and nylon, respectively. d Maximum force to dilate sections of a planar chain of beads consisting of 15 adjoining rings of n = 4 beads, threaded with nitinol and nylon for various T₀. Source data is available in Supplementary Data 2.

Fig. 4. Mechanical properties of larger beaded networks.

a A beaded column consisting of loops with n = 4 and elastomeric thread is stretched and compressed, revealing three regimes: linear elastic (yellow), strain stiffening (green), and superjamming (purple). Loading and unloading paths are marked with black and white arrows, respectively. Scale bar, 30 mm. b μ-CT imaging of the column in a with in-situ forcing in the following configurations: jammed (i), neutral (ii), and stretched (iii). Scale bars, 10 mm. c A beam beaded with loops of n = 3 is threaded with SMA wire, which contracts ~4% when heated by electric current. We perform a 3-point bending test and report the mean fitted slopes (F/δ) for repeated trials, with and without voltage applied. Scale bar, 15 mm. d Photograph of a catenary dome beaded using loops of n = 5, 6, and 7. The surface is constructed with large acrylic beads (R = 10 mm), waxed polyester cord, and is subject to gravity. Bending via the distribution of characteristic slack in the network causes localized stiffening, leading to metastability and many possible rigid conformations. Scale bar, 100 mm. e Photograph of a rigid, egg-crate-like surface beaded using loops of n = 4, 6, and 8. The surface is constructed with small acrylic beads (R = 6 mm). Up and down states are marked in white and gray, respectively. Photographs of the corresponding structures are shown in i–iv. Scale bar, 30 mm. Source data is available in Supplementary Data 3.