Skip to main content

Thank you for visiting nature.com. 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.

  • Article
  • Published:

Modular chiral origami metamaterials

Nature volume 640, pages 931–940 (2025)Cite this article

Subjects

Abstract

Metamaterials with multimodal deformation mechanisms resemble machines1,2, especially when endowed with autonomous functionality. A representative architected assembly, with tunable chirality, converts linear motion into rotation3. These chiral metamaterials with a machine-like dual modality have potential use in areas such as wave manipulation4, optical activity related to circular polarization5 and chiral active fluids6. However, the dual motions are essentially coupled and cannot be independently controlled. Moreover, they are restricted to small deformation, that is, strain ≤2%, which limits their applications. Here we establish modular chiral metamaterials, consisting of auxetic planar tessellations and origami-inspired columnar arrays, with decoupled actuation. Under single-degree-of-freedom actuation, the assembly twists between 0° and 90°, contracts in-plane up to 25% and shrinks out-of-plane more than 50%. Using experiments and simulations, we show that the deformation of the assembly involves in-plane twist and contraction dominated by the rotating-square tessellations and out-of-plane shrinkage dominated by the tubular Kresling origami arrays. Moreover, we demonstrate two distinct actuation conditions: twist with free translation and linear displacement with free rotation. Our metamaterial is built on a highly modular assembly, which enables reprogrammable instability, local chirality control, tunable loading capacity and scalability. Our concept provides routes towards multimodal, multistable and reprogrammable machines, with applications in robotic transformers, thermoregulation, mechanical memories in hysteresis loops, non-commutative state transition and plug-and-play functional assemblies for energy absorption and information encryption.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

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

Fig. 1: The multimodal metamaterial composed of hinged tessellations and chiral origami-inspired lattice cells.
Fig. 2: Experimental validation of multimodal deformation using a rotational actuator with free translation.
Fig. 3: Experiment of multimodal deformation using a linear displacement actuation with free rotation.
Fig. 4: Surrogate model simulation for multimodal deformations of the modular assembly.
Fig. 5: Plug-and-play strategy for creating reprogrammable metamaterials.
Fig. 6: Scope of multimodal origami metamaterials.

Similar content being viewed by others

Data availability

The experimental data supporting the findings of this study are openly available at Zenodo56 (https://doi.org/10.5281/zenodo.14676200). Source data are provided with this paper.

Code availability

The simulation codes supporting the findings of this study are openly available at Zenodo56 (https://doi.org/10.5281/zenodo.14676200).

References

  1. McEvoy, M. A. & Correll, N. Materials that couple sensing, actuation, computation, and communication. Science 347, 1261689 (2015).

    CAS  PubMed  Google Scholar 

  2. Mirkhalaf, M. & Rafsanjani, A. Harnessing machine mechanisms to continuously reprogram metamaterials. Matter 6, 3719–3731 (2023).

    Google Scholar 

  3. Frenzel, T., Kadic, M. & Wegener, M. Three-dimensional mechanical metamaterials with a twist. Science 358, 1072–1074 (2017).

    ADS  CAS  PubMed  Google Scholar 

  4. Yasuda, H. et al. Origami-based impact mitigation via rarefaction solitary wave creation. Sci. Adv. 5, eaau2835 (2019).

    ADS  PubMed  PubMed Central  Google Scholar 

  5. Gansel, J. K. et al. Gold helix photonic metamaterial as broadband circular polarizer. Science 325, 1513–1515 (2009).

    ADS  CAS  PubMed  Google Scholar 

  6. Banerjee, D., Souslov, A., Abanov, A. G. & Vitelli, V. Odd viscosity in chiral active fluids. Nat. Commun. 8, 1573 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  7. Fleck, N. A., Deshpande, V. S. & Ashby, M. F. Micro-architectured materials: past, present and future. Proc. R. Soc. A Math. Phys. Eng. Sci. 466, 2495–2516 (2010).

    ADS  CAS  Google Scholar 

  8. Deshpande, V. S., Fleck, N. A. & Ashby, M. F. Effective properties of the octet-truss lattice material. J. Mech. Phys. Solids 49, 1747–1769 (2001).

    ADS  CAS  Google Scholar 

  9. Berger, J., Wadley, H. G. N. & McMeeking, R. M. Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness. Nature 543, 533–537 (2017).

    ADS  CAS  PubMed  Google Scholar 

  10. Deshpande, V. S., Ashby, M. F. & Fleck, N. A. Foam topology: bending versus stretching dominated architectures. Acta Materialia 49, 1035–1040 (2001).

    ADS  CAS  Google Scholar 

  11. Gibson, L. J. & Ashby, M. F. Cellular Solids: Structure and Properties 2nd edn (Cambridge Univ. Press, 1999).

  12. Jiao, P., Mueller, J., Raney, J. R., Zheng, X. & Alavi, A. H. Mechanical metamaterials and beyond. Nat. Commun.14, 6004 (2023).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  13. Zheng, X. et al. Ultralight, ultrastiff mechanical metamaterials. Science 344, 1373–1377 (2014).

    ADS  CAS  PubMed  Google Scholar 

  14. Portela, C. M. et al. Supersonic impact resilience of nanoarchitected carbon. Nat. Mater. 20, 1491–1497 (2021).

    ADS  CAS  PubMed  Google Scholar 

  15. Shaikeea, A. J. D., Cui, H., O’Masta, M., Zheng, X. R. & Deshpande, V. S. The toughness of mechanical metamaterials. Nat. Mater. 21, 297–304 (2022).

    ADS  CAS  PubMed  Google Scholar 

  16. Hatch, H. W., Stillinger, F. H. & Debenedetti, P. G. Chiral symmetry breaking in a microscopic model with asymmetric autocatalysis and inhibition. J. Chem. Phys. 133, 224502 (2010).

    ADS  PubMed  Google Scholar 

  17. Feng, H. et al. Helical structures with switchable and hierarchical chirality. Appl. Phys. Lett. 116, 194102 (2020).

    ADS  Google Scholar 

  18. Frenzel, T. et al. Large characteristic lengths in 3D chiral elastic metamaterials. Commun. Mater. 2, 4 (2021).

    Google Scholar 

  19. Choi, G. P. T., Dudte, L. H. & Mahadevan, L. Programming shape using kirigami tessellations. Nat. Mater. 18, 999–1004 (2019).

    ADS  CAS  PubMed  Google Scholar 

  20. Misseroni, D. et al. Origami engineering. Nat. Rev. Methods Primers 4, 40 (2024).

    CAS  Google Scholar 

  21. Blees, M. K. et al. Graphene kirigami. Nature 524, 204–207 (2015).

    ADS  CAS  PubMed  Google Scholar 

  22. Schroeder, T. B. H. et al. An electric-eel-inspired soft power source from stacked hydrogels. Nature 552, 214–218 (2017).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  23. Bertoldi, K., Vitelli, V., Christensen, J. & van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater. 2, 17066 (2017).

    ADS  CAS  Google Scholar 

  24. Cui, J. et al. Nanomagnetic encoding of shape-morphing micromachines. Nature 575, 164–168 (2019).

    ADS  CAS  PubMed  Google Scholar 

  25. Overvelde, J. T. B., Weaver, J. C., Hoberman, C. & Bertoldi, K. Rational design of reconfigurable prismatic architected materials. Nature 541, 347–352 (2017).

    ADS  CAS  PubMed  Google Scholar 

  26. Hu, Z. et al. Engineering zero modes in transformable mechanical metamaterials. Nat. Commun. 14, 1266 (2023).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  27. Melancon, D., Gorissen, B., García-Mora, C. J., Hoberman, C. & Bertoldi, K. Multistable inflatable origami structures at the metre scale. Nature 592, 545–550 (2021).

    ADS  CAS  PubMed  Google Scholar 

  28. Overvelde, J. T. B. et al. A three-dimensional actuated origami-inspired transformable metamaterial with multiple degrees of freedom. Nat. Commun. 7, 10929 (2016).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  29. Li, Y. et al. Adaptive hierarchical origami-based metastructures. Nat. Commun. 15, 6247 (2024).

    CAS  PubMed  PubMed Central  Google Scholar 

  30. Kim, Y., Yuk, H., Zhao, R., Chester, S. A. & Zhao, X. Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature 558, 274–279 (2018).

    ADS  CAS  PubMed  Google Scholar 

  31. Kim, Y. & Zhao, X. Magnetic soft materials and robots. Chem. Rev. 122, 5317–5364 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  32. Xia, X., Spadaccini, C. M. & Greer, J. R. Responsive materials architected in space and time. Nat. Rev. Mater. 7, 683–701 (2022).

    ADS  PubMed  PubMed Central  Google Scholar 

  33. Jenett, B. et al. Discretely assembled mechanical metamaterials. Sci. Adv. 6, eabc9943 (2020).

    ADS  PubMed  PubMed Central  Google Scholar 

  34. Chen, T., Pauly, M. & Reis, P. M. A reprogrammable mechanical metamaterial with stable memory. Nature 589, 386–390 (2021).

    ADS  CAS  PubMed  Google Scholar 

  35. Zhang, Y., Velay-Lizancos, M., Restrepo, D., Mankame, N. D. & Zavattieri, P. D. Architected material analogs for shape memory alloys. Matter 4, 1990–2012 (2021).

    CAS  Google Scholar 

  36. Liu, K., Pratapa, P. P., Misseroni, D., Tachi, T. & Paulino, G. H. Triclinic metamaterials by tristable origami with reprogrammable frustration. Adv. Mater. 34, 2107998 (2022).

    CAS  Google Scholar 

  37. Schenk, M. & Guest, S. D. Geometry of miura-folded metamaterials. Proc. Natl Acad. Sci. USA 110, 3276–3281 (2013).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  38. Liu, K. & Paulino, G. H. Nonlinear mechanics of non-rigid origami: an efficient computational approach. Proc. R. Soc. A Math. Phys. Eng. Sci. 473, 20170348 (2017).

    ADS  MathSciNet  CAS  Google Scholar 

  39. Rafsanjani, A., Bertoldi, K. & Studart, A. R. Programming soft robots with flexible mechanical metamaterials. Sci. Robot. 4, eaav7874 (2019).

    PubMed  Google Scholar 

  40. Cui, H. et al. Design and printing of proprioceptive three-dimensional architected robotic metamaterials. Science 376, 1287–1293 (2022).

    ADS  CAS  PubMed  Google Scholar 

  41. Yoder, Z., Rumley, E. H., Schmidt, I., Rothemund, P. & Keplinger, C. Hexagonal electrohydraulic modules for rapidly reconfigurable high-speed robots. Sci. Robot. 9, eadl3546 (2024).

    PubMed  Google Scholar 

  42. Baines, R., Fish, F., Bongard, J. & Kramer-Bottiglio, R. Robots that evolve on demand. Nat. Rev. Mater. 9, 822–835 (2024).

    Google Scholar 

  43. Yin, X., Yang, R., Tan, G. & Fan, S. Terrestrial radiative cooling: using the cold universe as a renewable and sustainable energy source. Science 370, 786–791 (2020).

    ADS  CAS  PubMed  Google Scholar 

  44. Mandal, J. et al. Scalable, “dip-and-dry” fabrication of a wide-angle plasmonic selective absorber for high-efficiency solar-thermal energy conversion. Adv. Mater. 29, 1702156 (2017).

    Google Scholar 

  45. Mandal, J. et al. Porous polymers with switchable optical transmittance for optical and thermal regulation. Joule 3, 3088–3099 (2019).

    CAS  Google Scholar 

  46. Visintin, A. Differential Models of Hysteresis (Springer, 2013).

  47. Preisach, F. Über die magnetische nachwirkung. Z. Phys. 94, 277–302 (1935).

    ADS  Google Scholar 

  48. Yasuda, H. et al. Mechanical computing. Nature 598, 39–48 (2021).

    ADS  CAS  PubMed  Google Scholar 

  49. Mungan, M. Putting memories on paper. Proc. Natl Acad. Sci. USA 119, e2208743119 (2022).

    CAS  PubMed  PubMed Central  Google Scholar 

  50. Liu, J. et al. Controlled pathways and sequential information processing in serially coupled mechanical hysterons. Proc. Natl Acad. Sci. USA 121, e2308414121 (2024).

    CAS  PubMed  PubMed Central  Google Scholar 

  51. Kresling, B. Natural twist buckling in shells: from the Hawkmoth’s bellows to the deployable Kresling-pattern and cylindrical Miura-ori (2008). In Proc. 6th International Conference on Computation of Shell and Spatial Structures IASS-IACM: “Spanning Nano to Mega” (eds Abel, J.F. & Cooke, J. R.) 18–21 (Cornell Univ. Press, 2008).

  52. Yasuda, H., Tachi, T., Lee, M. & Yang, J. Origami-based tunable truss structures for non-volatile mechanical memory operation. Nat. Commun. 8, 962 (2017).

    ADS  PubMed  PubMed Central  Google Scholar 

  53. Zhai, Z., Wang, Y. & Jiang, H. Origami-inspired, on-demand deployable and collapsible mechanical metamaterials with tunable stiffness. Proc. Natl Acad. Sci. USA 115, 2032–2037 (2018).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  54. Lang, R. J. Twists, Tilings, and Tessellations: Mathematical Methods for Geometric Origami (CRC Press, 2017).

  55. Qi, H., Joyce, K. & Boyce, M. Durometer hardness and the stress-strain behavior of elastomeric materials. Rubber Chem. Technol. 76, 419–435 (2003).

    CAS  Google Scholar 

  56. Paulino, G. H. et al. Super-modular chiral origami metamaterials. Zenodo https://doi.org/10.5281/zenodo.14676200 (2025).

  57. Zang, S., Misseroni, D., Zhao, T. & Paulino, G. H. Kresling origami mechanics explained: experiments and theory. J. Mech. Phys. Solids 188, 105630 (2024).

    MathSciNet  Google Scholar 

Download references

Acknowledgements

We thank B. Kresling (creator of the Kresling pattern), E.A. Paulino, S. Kahn, T. Tachi, C.M. Sharpless, J. Russ, L. Novelino and K.T. Liu for their discussions; P.T. Brun for assistance with the mechanical testing of the reprogrammable assembly; and Y. Rao for her comments and suggestions on the manuscript. This research was supported by Margareta E. Augustine Professorship of Engineering at Princeton University and the National Science Foundation under grant no. 2323276. We also acknowledge support from the Andlinger Center for Energy and the Environment, the Princeton Materials Institute, and the Council on Science and Technology at Princeton University.

Author information

Author notes

  1. These authors contributed equally: Tuo Zhao, Xiangxin Dang

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA

    Tuo Zhao, Xiangxin Dang, Shixi Zang, Jyotirmoy Mandal & Glaucio H. Paulino

  2. Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ, USA

    Konstantinos Manos & Minjie Chen

  3. Princeton Materials Institute, Princeton University, Princeton, NJ, USA

    Jyotirmoy Mandal & Glaucio H. Paulino

  4. Andlinger Center for Energy and the Environment, Princeton University, Princeton, NJ, USA

    Minjie Chen

Authors
  1. Tuo Zhao
    View author publications

    Search author on:PubMed Google Scholar

  2. Xiangxin Dang
    View author publications

    Search author on:PubMed Google Scholar

  3. Konstantinos Manos
    View author publications

    Search author on:PubMed Google Scholar

  4. Shixi Zang
    View author publications

    Search author on:PubMed Google Scholar

  5. Jyotirmoy Mandal
    View author publications

    Search author on:PubMed Google Scholar

  6. Minjie Chen
    View author publications

    Search author on:PubMed Google Scholar

  7. Glaucio H. Paulino
    View author publications

    Search author on:PubMed Google Scholar

Contributions

T.Z. and G.H.P. proposed and developed the research idea. T.Z. designed and fabricated the Kresling origami samples and tessellations. T.Z. and X.D. conceptualized the actuation of the origami assemblies. X.D. developed the computational framework, performed simulations, analysed the data and provided the Preisach model. T.Z. and S.Z. performed mechanical testing of the Kresling origami assemblies. K.M. and M.C. designed the magnetic drive hardware and software and T.Z. and K.M. performed the magnetic experiments. J.M. and G.H.P. originated the thermoregulation concept and T.Z. and S.Z. designed it. X.D. and S.Z. implemented non-commutative state transition experiments. G.H.P. supervised the project. All co-authors provided feedback and contributed to the paper.

Corresponding author

Correspondence to Glaucio H. Paulino.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Davide Bigoni, Suyi Li, Hiromi Yasuda and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Additional information

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 Modular lattice cell geometry.

a, From standard shell-based origami to the rod-based lattice unit. Visual comparison between a paper-folded Kresling origami (left) and a 3D-printed lattice prototype (right). The diameter of the rods is 1.5 mm (scale bar, 5 mm). b, Schematic of a 6-gon unit in the deployed state (left) and in the folded state (middle). The top view (right) of the unit highlights two twist angles, φ1 and φ0, which define the position of the top polygon in the two stable states. h1, deployed unit height; h0, folded unit height; u, displacement; c, valley rod length; b, mountain rod length; r, polygon radius. c, The strain energy of the unit versus twist angle obtained with the bar-and-hinge method. d, The height of the unit versus twist angle.

Extended Data Fig. 2 Schematics of mechanical test setups: boundary conditions and loading conditions.

a, Axial translation fixture for standard tests with displacement control. Left and right: for results in left and right of Fig. 6e, respectively. Middle: for Fig. 5. b, Dedicated fixture for rotational test with free translation57. This fixture is used for obtaining results in Figs. 2, 6d, Extended Data Fig. 8, and Supplementary Fig. S4. c, Alternative fixtures for linear displacement with free rotation. Left: Supplementary Fig. S5. Middle: Supplementary Fig. S6. Right: Fig. 3 and Supplementary Fig. S7.

Extended Data Fig. 3 Surrogate model simulation for multimodal deformations of the chiral modular cells.

a, The modular cells (frames) and the origami models (shells). b, Mechanical springs in the surrogate model. c, Torque-twist-angle curves from the twisting simulation of three cells of the same geometry but different material properties. d, Force-displacement curves from the compression simulation of three cells of the same geometry but different material properties.

Extended Data Fig. 4 Surrogate model simulation for multimodal deformations of the chiral modular columns with different constituent cells.

a, Torque versus cumulative twist angle from the twisting simulation of the columns. b, Deformation snapshots of the twisted columns. The two boxes indicate the configurations with corresponding experimental results (Extended Data Fig. 5). c, Force versus displacement from the compression simulation of the columns. d, Deformation snapshots of the compressed columns.

Extended Data Fig. 5 Twisting experiments of two columns that differ by their chiral modular arrangement and material composition.

a, Surrogate model simulations. b, Experimental results. c, Snapshots illustrating the twisting experiment with free translation. d, Experimental results of torque versus cumulative twist angle.

Source data

Extended Data Fig. 6 Electrical system for the precise control of the magnetically actuated robotic metamaterial.

a, Experimental setup consisting of a dc power source, a scalable power converter, and a set of copper coils. b, Modular power converter prototype comprising six individual power electronic building blocks. c, 3-D Helmholtz coil structure made of six circular-winding pairs; each pair consists of two windings connected in series. d, Scalable power-converter topology consisting of six full-bridge submodules to precisely control the current of each winding pair. e, System block diagram showing the closed loop current-control scheme; the winding currents are sensed locally in each submodule using shunt resistors. A proportional-integral controller is implemented on a microcontroller card resulting in an equivalent first order reference-to-winding current system. Each coil is modeled by an inductance value L and a resistance R representing the resistivity of the copper wire. The controller gains are selected as \({k}_{p}=L/{t}_{r}ln9\) and \({k}_{i}=R/{t}_{r}ln9\) to accomplish a 10% to 90% current rise time of tr = 1.5 ms. A pulse width modulator (PWM) employing a 10 kHz triangular carrier wave is used to generate the signals controlling the states of the individual power switches.

Extended Data Fig. 7 The optically augmented multistable origami assembly.

a, Digital image of the prototype in the deployed state. b, Prototype in the folded state. c, Interactive algorithm for parametric modelling with calculation of the origami cell in the deployed state. d, Interactive algorithm for parametric modelling with calculation of the origami cell in the folded state.

Extended Data Fig. 8 Non-commutative state transition of the two-layer chiral metamaterial.

a, The possible states of the metamaterial. A two-bit number is used to indicate the global states, with each bit representing an entire layer. For each bit, the digit 1 indicates that the layer is deployed, and the digit 0 indicates that the layer is folded. b–e, Experimental loading curves for state transitions (b) starting from 11 with a anticlockwise rotation followed by a clockwise rotation, (c) starting from 11 with a clockwise rotation followed by a anticlockwise rotation, (d) starting from 00 with a clockwise rotation followed by a anticlockwise rotation, (e) starting from 00 with a anticlockwise rotation followed by a clockwise rotation. The peak torques that trigger the state transitions are indicated in the plots.

Source data

Supplementary information

Supplementary Information (download PDF )

This file contains Supplementary Figs. 1–18, Supplementary Table 1 and additional references.

Peer Review File (download PDF )

Supplementary Video 1 (download MP4 )

Twist experiment.

Supplementary Video 2 (download MP4 )

Linear displacement experiment.

Supplementary Video 3 (download MP4 )

Multimodal metamaterial simulations.

Supplementary Video 4 (download MP4 )

Plug-and-play: reconfigurable assemblies.

Supplementary Video 5 (download MP4 )

Magnetic robot transformer.

Supplementary Video 6 (download MP4 )

Non-commutative state transition.

Source data

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, T., Dang, X., Manos, K. et al. Modular chiral origami metamaterials. Nature 640, 931–940 (2025). https://doi.org/10.1038/s41586-025-08851-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Version of record:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41586-025-08851-0

This article is cited by

Search

Advanced search

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