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Structured fabrics with tunable mechanical properties


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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Fig. 1: The design and prototype of the architected chain mail fabrics.
Fig. 2: Bending and tensile tests with variable confining pressure.
Fig. 3: Micro-structural information obtained from simulations at different confining pressures.
Fig. 4: Shape reconfigurability, tunable impact resistance, and applications.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request and online (


  1. 1.

    Chen, X., Taylor, L. W. & Tsai, L. J. An overview on fabrication of three-dimensional woven fabric preforms for composites. Text. Res. J. 81, 932–944 (2011).

  2. 2.

    Engel, J. & Liu, C. Creation of a metallic micromachined chain mail fabric. J. Micromech. Microeng. 17, 551–556 (2007).

    ADS  Article  Google Scholar 

  3. 3.

    Tabiei, A. & Nilakantan, G. Ballistic impact of dry woven fabric composites: a review. Appl. Mech. Rev. 61, 010801 (2008).

    ADS  Article  Google Scholar 

  4. 4.

    Cai, L. et al. Warming up human body by nanoporous metallized polyethylene fabric. Nat. Commun. 8, 496 (2017).

    ADS  Article  Google Scholar 

  5. 5.

    Stoppa, M. & Chiolerio, A. Wearable electronics and smart fabrics: a critical review. Sensors 14, 11957–11992 (2014).

    ADS  CAS  Article  Google Scholar 

  6. 6.

    Mondal, S. Phase change materials for smart fabrics—an overview. Appl. Therm. Eng. 28, 1536–1550 (2008).

    CAS  Article  Google Scholar 

  7. 7.

    Gauvreau, B. et al. Color-changing and color-tunable photonic bandgap fiber fabrics. Opt. Express 16, 15677–15693 (2008).

    ADS  CAS  Article  Google Scholar 

  8. 8.

    Cherenack, K., Zysset, C., Kinkeldei, T., Münzenrieder, N. & Tröster, G. Woven electronic fibers with sensing and display functions for smart fabrics. Adv. Mater. 22, 5178–5182 (2010).

    CAS  Article  Google Scholar 

  9. 9.

    Cherenack, K. & van Pieterson, L. Smart fabrics: challenges and opportunities. J. Appl. Phys. 112, 091301 (2012).

    ADS  Article  Google Scholar 

  10. 10.

    Chen, J. et al. Micro-cable structured fabric for simultaneously harvesting solar and mechanical energy. Nat. Energy 1, 16138 (2016).

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Ploszajski, A. R., Jackson, R., Ransley, M. & Miodownik, M. 4D printing of magnetically functionalized chainmail for exoskeletal biomedical applications. MRS Adv. 4, 1361–1366 (2019).

    CAS  Article  Google Scholar 

  12. 12.

    Liu, A. J. & Nagel, S. R. Jamming is not just cool any more. Nature 396, 21 (1998).

    ADS  CAS  Article  Google Scholar 

  13. 13.

    Liu, A. J. & Nagel, S. R. The jamming transition and the marginally jammed solid. Annu. Rev. Condens. Matter Phys. 1, 347–369 (2010).

    ADS  Article  Google Scholar 

  14. 14.

    Bi, D., Zhang, J., Chakraborty, B. & Behringer, R. P. Jamming by shear. Nature 480, 355–358 (2011).

    ADS  CAS  Article  Google Scholar 

  15. 15.

    Jaeger, H. Celebrating Soft Matter’s 10th anniversary: toward jamming by design. Soft Matter 11, 12 (2015).

    ADS  CAS  Article  Google Scholar 

  16. 16.

    Narang, Y. S., Vlassak, J. J. & Howe, R. D. Mechanically versatile soft machines through laminar jamming. Adv. Funct. Mater. 28, 1707136 (2018).

    Article  Google Scholar 

  17. 17.

    Brown, E. et al. Universal robotic gripper based on the jamming of granular material. Proc. Natl Acad. Sci. USA 107, 18809–18814 (2010).

    ADS  CAS  Article  Google Scholar 

  18. 18.

    Wang, Y. et al. Architected lattices with adaptive energy absorption. Extreme Mech. Lett. 33, 100557 (2019).

    Article  Google Scholar 

  19. 19.

    Aejmelaeus-Lindstrom, P., Willmann, J., Tibbits, S., Gramazio, F. & Kohler, M. Jammed architectural structures: towards large-scale reversible construction. Granul. Matter 18, 28 (2016).

    Article  Google Scholar 

  20. 20.

    Brown, E., Nasto, A., Athanassiadis, A. G. & Jaeger, H. M. Strain stiffening in random packings of entangled granular chains. Phys. Rev. Lett. 108, 108302 (2012).

    ADS  Article  Google Scholar 

  21. 21.

    Dyskin, A. V., Estrin, Y., Kanel-Belov, A. J. & Pasternak, E. A new concept in design of materials and structures: assemblies of interlocked tetrahedron-shaped elements. Scr. Mater. 44, 2689–2694 (2001).

    CAS  Article  Google Scholar 

  22. 22.

    Dyskin, A. V., Pasternak, E. & Estrin, Y. Mortarless structures based on topological interlocking. Front. Struct. Civ. Eng. 6, 188–197 (2012).

    Google Scholar 

  23. 23.

    Zweben, C., Smith, W. & Wardle, M. Test methods for fiber tensile strength, composite flexural modulus, and properties of fabric-reinforced laminates. In Composite Materials: Testing and Design (Fifth Conference) 228–262 (1979).

  24. 24.

    Manti, M., Cacucciolo, V. & Cianchetti, M. Stiffening in soft robotics: a review of the state of the art. IEEE Robot. Autom. 23, 93–106 (2016).

    Article  Google Scholar 

  25. 25.

    Wang, L. et al. Controllable and reversible tuning of material rigidity for robot applications. Mater. Today 21, 563−576 (2018).

    Google Scholar 

  26. 26.

    Meng, H. & Li, G. A review of stimuli-responsive shape memory polymer composites. Polymer 54, 2199–2221 (2013).

    CAS  Article  Google Scholar 

  27. 27.

    White, T. J. & Broer, D. J. Programmable and adaptive mechanics with liquid crystal polymer networks and elastomers. Nat. Mater. 14, 1087–1098 (2015).

    ADS  CAS  Article  Google Scholar 

  28. 28.

    Jackson, J. A. et al. Field responsive mechanical metamaterials. Sci. Adv. 4, eaau6419 (2018).

    ADS  CAS  Article  Google Scholar 

  29. 29.

    Biggs, J. et al. Electroactive polymers: developments of and perspectives for dielectric elastomers. Angew. Chem. Int. Ed. 52, 9409–9421 (2013).

    CAS  Article  Google Scholar 

  30. 30.

    Kawamoto, R., Andò, E., Viggiani, G. & Andrade, J. E. Level set discrete element method for three-dimensional computations with triaxial case study. J. Mech. Phys. Solids 91, 1–13 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  31. 31.

    Kawamoto, R., Andò, E., Viggiani, G. & Andrade, J. E. All you need is shape: predicting shear banding in sand with LS-DEM. J. Mech. Phys. Solids 111, 375–392 (2018).

    ADS  Article  Google Scholar 

  32. 32.

    Li, L., Marteau, E. & Andrade, J. Capturing the inter-particle force distribution in granular material using LS-DEM. Granul. Matter 21, 43 (2019).

    Article  Google Scholar 

  33. 33.

    Cundall, P. A. & Strack, O. D. L. A discrete numerical model for granular assemblies. Geotechnique 29, 47–65 (1979).

    Article  Google Scholar 

  34. 34.

    Majmudar, T. S. & Behringer, R. P. Contact force measurements and stress-induced anisotropy in granular materials. Nature 435, 1079–1082 (2005).

    ADS  CAS  Article  Google Scholar 

  35. 35.

    Silbert, L. E. et al. Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 051302 (2001).

    ADS  CAS  Article  Google Scholar 

  36. 36.

    Miskin, M. Z. & Jaeger, H. M. Adapting granular materials through artificial evolution. Nat. Mater. 12, 326–331 (2013).

    ADS  CAS  Article  Google Scholar 

  37. 37.

    Pratapa, P. P., Liu, K. & Paulino, H. Geometric mechanics of origami patterns exhibiting Poisson’s ratio switch by breaking mountain and valley assignment. Phys. Rev. Lett. 122, 155501 (2019).

    ADS  MathSciNet  CAS  Article  Google Scholar 

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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.

Author information




Y.W. and C.D. designed the sample structure and the experiments. Y.W. fabricated the sample, performed the experiments and analysed experimental data. L.L. and J.E.A. designed the LS-DEM model. L.L. performed the LS-DEM simulations and analysed numerical results. D.H. printed the metallic chain mail. Y.W., L.L. and C.D. wrote the manuscript. All authors interpreted the results and reviewed the manuscript.

Corresponding author

Correspondence to Chiara Daraio.

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Competing interests

The authors declare no competing interests.

Additional information

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

Extended Data Fig. 1 Construction of the ‘digital twin’ and the envelope.

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.

Extended Data Fig. 3 Details of the 3D architected particles and fabrics.

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.

Extended Data Fig. 4 Details of the classical chain mail fabrics.

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.

Extended Data Table 1 Packing fraction of different fabric sheets under various confining pressures, and fitting parameters used for the power-law relation shown in Fig. 3g
Extended Data Table 2 Average dimensions computed from four separate simulations
Extended Data Table 3 Values of the model parameters used in this study
Extended Data Table 4 The Poisson’s ratio obtained during uni-axial tensile tests under different pressures for fabrics with three particle geometries

Supplementary information

Video 1

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).

Video 2

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).

Video 3

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.

Video 4

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).

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