Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  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).

    Article  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  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).

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  Google Scholar 

  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. 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).

    Article  ADS  Google Scholar 

  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).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  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).

    Article  ADS  MathSciNet  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  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).

    Article  ADS  MathSciNet  CAS  Google Scholar 

Download references


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

Authors and Affiliations



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.

Ethics declarations

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.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Li, L., Hofmann, D. et al. Structured fabrics with tunable mechanical properties. Nature 596, 238–243 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing