Structured fabrics, such as woven sheets or chain mail armours, derive their properties both from the constitutive materials and their geometry1,2. Their design can target desirable characteristics, such as high impact resistance, thermal regulation, or electrical conductivity3,4,5. Once realized, however, the fabrics’ properties are usually fixed. Here we demonstrate structured fabrics with tunable bending modulus, consisting of three-dimensional particles arranged into layered chain mails. The chain mails conform to complex shapes2, but when pressure is exerted at their boundaries, the particles interlock and the chain mails jam. We show that, with small external pressure (about 93 kilopascals), the sheets become more than 25 times stiffer than in their relaxed configuration. This dramatic increase in bending resistance arises because the interlocking particles have high tensile resistance, unlike what is found for loose granular media. We use discrete-element simulations to relate the chain mail’s micro-structure to macroscale properties and to interpret experimental measurements. We find that chain mails, consisting of different non-convex granular particles, undergo a jamming phase transition that is described by a characteristic power-law function akin to the behaviour of conventional convex media. Our work provides routes towards lightweight, tunable and adaptive fabrics, with potential applications in wearable exoskeletons, haptic architectures and reconfigurable medical supports.
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The data that support the findings of this study are available from the corresponding author upon reasonable request and online (https://github.com/Daraio-lab/StructuredFabricsTunable-WangY).
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We thank K. Liu for discussions; A. Pate, H. Ramirez and M. Zuleta for printing the aluminum chain mails ; D. Ruffatto for helping with printing early-stage prototypes; and S. Fan for assistance with photographing the 3D-printed sample in Figs. 1d, f and 4a, b. Y.W and C.D. acknowledge support from the Foster and Coco Stanback Space Innovation fund, Facebook and the Army Research Office grant W911NF-17-1-0147. L.L. and J.E.A. acknowledge support from the Army Research Office (MURI grant number W911NF-19-1-0245). This research was carried out at the California Institute of Technology and the Jet Propulsion Laboratory under a contract with the National Aeronautics and Space Administration, and funded through the President’s and Director’s Fund Program. Computational resources were provided by the High Performance Computing Center at Caltech.
The authors declare no competing interests.
Peer review information Nature thanks Laurent Orgeas and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
a, The actual particle geometry (left) and the corresponding nodes and surface triangulations of the constructed digital twin (right). b, The corresponding ‘grids’ of the constructed digital twin with colour indicating the signed shortest distance to the particle surface. c, d, The initial configurations of the envelopes (represented by connected spheres) and of the granular assemblies with (c) and without (d) topological interlocking. The centroids of three adjacent spheres form a triangle with surface area A and in-ward surface normal n. e, The probability distribution of the radii of the constituent membrane spheres of the envelope used for the interlocked fabric sheet (blue, c) and non-interlocked assembly (red, d). The notation ±0.025 indicates the lower and upper bound for each value shown on the x axis.
Extended Data Fig. 2 The bending test simulation and illustration of how we categorized each contact into either the ‘compressive’ or ‘tensile’ type.
a, Evolution of total kinetic energy (blue) and total contact number (red) of all constituent particles of a fabric sheet under two confining pressures: 13 kPa (upper panel) and 93 kPa (lower panel). b, Evolution of total contact number for the same fabric sheet during the ‘isotropic compression only’ simulation stage for six different applied confining pressures. c, Evolution of average deflection of loaded particles during the ‘three-point bending added’ simulation stage for the same six different applied confining pressures. d, In each of the subfigures, F is the total contact force vector and n1 and n2 are vectors pointing from the contact position to the respective centroid location of each contact particle.
Left column, Probability distribution of the digital twin’s edge lengths for all five additionally considered shapes (coloured in red) in comparison to that of the hollow octahedron (coloured in blue). In the inset, S and N represent the total surface area of the considered particle geometry and the number of nodes of the corresponding digital twin, respectively, while S0 and N0 represent those of the hollow octahedron and its digital twin. Right column, the corresponding assembled sheets (one layer) together with a closer look at the associated interlocking pattern.
The same comparison as in Extended Data Fig. 4 for classical chain mails consisting ring-shaped (a) and square-shaped particles (b). Left column, probability distribution of the digital twin’s edge lengths for two different chainmail shapes (coloured in red) in comparison to that of the hollow octahedron (coloured in blue). Right column, the corresponding assembled chain mail sheets (one layer) together with a closer look at the associated interlocking pattern.
Extended Data Fig. 5 Comparing experimental and numerical results of two-layer fabrics consisting of particles of different shapes and loaded along different directions.
a, Comparison between experimental and simulation results on fabrics consisting of interlocking particles constructed from three orthogonal rings. b, c, Bending and tensile moduli along different directions for fabrics consisting of particles constructed from three orthogonal rings (b) and cubic frame (c). The error bars shown in (a) and (b) represent the standard deviations obtained from five separate experiments and four separate simulations.
A LS-DEM simulation showing two fabric layers when a confining pressure P = 13 kPa (top) is applied, followed by a three-point bending test (bottom).
A LS-DEM simulation showing two fabric layers when a confining pressure P = 93 kPa (top) is applied, followed by a three-point bending test (bottom).
An experiment captured by high-speed camera (100 times playback) showing a stainless steel bead impacting at 3 m/s onto the fabrics at zero confining pressure.
An experiment captured by high-speed camera (100 times playback) showing a stainless steel bead impacting at 3 m/s onto the fabrics at 67 kPa confining pressure.
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Wang, Y., Li, L., Hofmann, D. et al. Structured fabrics with tunable mechanical properties. Nature 596, 238–243 (2021). https://doi.org/10.1038/s41586-021-03698-7
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