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.

  • Perspective
  • Published:

Performance metrics for shape-morphing devices

Nature Reviews Materials volume 9, pages 738–751 (2024)Cite this article

Subjects

Abstract

Shape-morphing devices, with their capacity to undergo structural transformations, are on the verge of revolutionizing multiple domains, from human–machine interfaces to biomedical and aerospace applications. This Perspective classifies shape-morphing devices into two categories: pattern-to-pattern shape-morphing devices that deform from a starting shape to a predefined set of one or more deformed shapes, and programmable shape-morphing devices that can morph into different shapes on demand. We highlight the need for standardized assessment approaches to compare the performance of different shape-morphing devices and introduce an array of proposed metrics that are tailored to assess the functionality of these devices at the material, device and system levels. Notably, we propose a mathematical metric to quantify the complexity of a surface and a set of standard surfaces for evaluating programmable shape-morphing devices, providing objective benchmarks for this expanding field.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Fig. 1: Pattern-to-pattern shape morphing and dynamic programmable shape morphing.
Fig. 2: Performance metrics.
Fig. 3: Performance metrics of selected shape-morphing devices.
Fig. 4: Method to evaluate surface complexity.
Fig. 5: Proposed reference parametric surfaces.

Similar content being viewed by others

References

  1. Shah, D. et al. Shape changing robots: bioinspiration, simulation, and physical realization. Adv. Mater. 33, 2002882 (2021).

    Article  CAS  Google Scholar 

  2. Boston, D. M., Phillips, F. R., Henry, T. C. & Arrieta, A. F. Spanwise wing morphing using multistable cellular metastructures. Extrem. Mech. Lett. 53, 101706 (2022).

    Article  Google Scholar 

  3. Sofla, A., Meguid, S., Tan, K. & Yeo, W. Shape morphing of aircraft wing: status and challenges. Mater. Des. 31, 1284–1292 (2010).

    Article  CAS  Google Scholar 

  4. Abdullah, Y. S. & Al-Alwan, H. A. Smart material systems and adaptiveness in architecture. Ain Shams Eng. J. 10, 623–638 (2019).

    Article  Google Scholar 

  5. Sobczyk, M., Wiesenhütter, S., Noennig, J. R. & Wallmersperger, T. Smart materials in architecture for actuator and sensor applications: a review. J. Intell. Mater. Syst. Struct. 33, 379–399 (2022).

    Article  CAS  Google Scholar 

  6. Walther, A. From responsive to adaptive and interactive materials and materials systems: a roadmap. Adv. Mater. 32, 1905111 (2020).

    Article  CAS  Google Scholar 

  7. Shahbazi, M., Jäger, H., Ettelaie, R., Mohammadi, A. & Kashi, P. A. Multimaterial 3D printing of self-assembling smart thermo-responsive polymers into 4D printed objects: a review. Addit. Manuf. 71, 103598 (2023).

    CAS  Google Scholar 

  8. Chen, X. et al. Harnessing 4D printing bioscaffolds for advanced orthopedics. Small 18, 2106824 (2022).

    Article  CAS  Google Scholar 

  9. Kirillova, A. & Ionov, L. Shape-changing polymers for biomedical applications. J. Mater. Chem. B 7, 1597–1624 (2019).

    Article  CAS  PubMed  Google Scholar 

  10. Viola, J. M. et al. Guiding cell network assembly using shape‐morphing hydrogels. Adv. Mater. 32, 2002195 (2020).

    Article  CAS  Google Scholar 

  11. Bertoldi, K., Vitelli, V., Christensen, J. & Van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater. 2, 1–11 (2017).

    Article  Google Scholar 

  12. Jiang, S. et al. Flexible metamaterial electronics. Adv. Mater. 34, 2200070 (2022).

    Article  CAS  Google Scholar 

  13. Jeon, S.-J., Hauser, A. W. & Hayward, R. C. Shape-morphing materials from stimuli-responsive hydrogel hybrids. Acc. Chem. Res. 50, 161–169 (2017).

    Article  CAS  PubMed  Google Scholar 

  14. Siéfert, E., Reyssat, E., Bico, J. & Roman, B. Bio-inspired pneumatic shape-morphing elastomers. Nat. Mater. 18, 24–28 (2019).

    Article  PubMed  Google Scholar 

  15. 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). Three-dimensional-printed magnetic-driven pattern-to-pattern shape-morphing device with fast response and high surface complexity.

    Article  CAS  PubMed  Google Scholar 

  16. Lin, H.-T., Leisk, G. G. & Trimmer, B. GoQBot: a caterpillar-inspired soft-bodied rolling robot. Bioinspir. Biomim. 6, 026007 (2011).

    Article  PubMed  Google Scholar 

  17. Yim, S. & Sitti, M. Shape-programmable soft capsule robots for semi-implantable drug delivery. IEEE Trans. Robot. 28, 1198–1202 (2012).

    Article  Google Scholar 

  18. Han, B. et al. Reprogrammable soft robot actuation by synergistic magnetic and light fields. Adv. Funct. Mater. 32, 2110997 (2022).

    Article  CAS  Google Scholar 

  19. Li, C. et al. Fast and programmable locomotion of hydrogel–metal hybrids under light and magnetic fields. Sci. Robot. 5, eabb9822 (2020).

    Article  PubMed  Google Scholar 

  20. Wang, J., Chen, G., Zhang, Z., Suo, J. & Wang, H. Wireless multiplexing control based on magnetic coupling resonance and its applications in robot. J. Mech. Robot. 14, 011009 (2022).

    Article  Google Scholar 

  21. Xin, C. et al. Environmentally adaptive shape-morphing microrobots for localized cancer cell treatment. ACS Nano 15, 18048–18059 (2021).

    Article  CAS  PubMed  Google Scholar 

  22. Wang, C., Wu, Y., Dong, X., Armacki, M. & Sitti, M. In situ sensing physiological properties of biological tissues using wireless miniature soft robots. Sci. Adv. 9, eadg3988 (2023).

    Article  CAS  PubMed  Google Scholar 

  23. Wang, J. et al. Pneumatic non-equibiaxial cell stretching device with live-cell imaging. IEEE Trans. Biomed. Eng. 71, 820–830 (2023).

    Article  Google Scholar 

  24. Costanza, G. & Tata, M. E. Shape memory alloys for aerospace, recent developments, and new applications: a short review. Materials 13, 1856 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Feng, R. et al. Soft robotic perspective and concept for planetary small body exploration. Soft Robot. 9, 889–899 (2022).

    Article  PubMed  Google Scholar 

  26. Kretzer, M. Information Materials: Smart Materials for Adaptive Architecture (Springer, 2016).

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

    Article  CAS  Google Scholar 

  28. Chai, J. et al. Thermoregulatory clothing with temperature-adaptive multimodal body heat regulation. Cell Rep. Phys. Sci. 3, 100958 (2022).

    Article  Google Scholar 

  29. Ford, M. J. et al. A multifunctional shape-morphing elastomer with liquid metal inclusions. Proc. Natl Acad. Sci. USA 116, 21438–21444 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Kotikian, A., Truby, R. L., Boley, J. W., White, T. J. & Lewis, J. A. 3D printing of liquid crystal elastomeric actuators with spatially programmed nematic order. Adv. Mater. 30, 1706164 (2018).

    Article  Google Scholar 

  31. Yu, C. et al. Electronically programmable, reversible shape change in two- and three-dimensional hydrogel structures. Adv. Mater. 25, 1541–1546 (2013).

    Article  CAS  PubMed  Google Scholar 

  32. Banerjee, H., Suhail, M. & Ren, H. Hydrogel actuators and sensors for biomedical soft robots: brief overview with impending challenges. Biomimetics 3, 15 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  33. Nojoomi, A., Arslan, H., Lee, K. & Yum, K. Bioinspired 3D structures with programmable morphologies and motions. Nat. Commun. 9, 3705 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  34. Zhang, M. et al. Hydrogel muscles powering reconfigurable micro-metastructures with wide-spectrum programmability. Nat. Mater. 22, 1243–1252 (2023).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Seffen, K. Mechanical memory metal: a novel material for developing morphing engineering structures. Scr. Mater. 55, 411–414 (2006).

    Article  CAS  Google Scholar 

  36. Neville, R. M. et al. A kirigami shape memory polymer honeycomb concept for deployment. Smart Mater. Struct. 26, 05LT03 (2017).

    Article  Google Scholar 

  37. Mao, Y. et al. 3D printed reversible shape changing components with stimuli responsive materials. Sci. Rep. 6, 24761 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Wu, J. et al. Multi-shape active composites by 3D printing of digital shape memory polymers. Sci. Rep. 6, 24224 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  39. Liu, X. et al. Recent advances in stimuli‐responsive shape‐morphing hydrogels. Adv. Funct. Mater. 32, 2203323 (2022).

    Article  CAS  Google Scholar 

  40. Wang, E., Desai, M. S. & Lee, S.-W. Light-controlled graphene–elastin composite hydrogel actuators. Nano Lett. 13, 2826–2830 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Lee, E., Kim, D., Kim, H. & Yoon, J. Photothermally driven fast responding photo-actuators fabricated with comb-type hydrogels and magnetite nanoparticles. Sci. Rep. 5, 15124 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Chen, J., Jiang, J., Weber, J., Gimenez-Pinto, V. & Peng, C. Shape morphing by topological patterns and profiles in laser-cut liquid crystal elastomer kirigami. ACS Appl. Mater. Interfaces 15, 4538–4548 (2023).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  44. Alapan, Y., Karacakol, A. C., Guzelhan, S. N., Isik, I. & Sitti, M. Reprogrammable shape morphing of magnetic soft machines. Sci. Adv. 6, eabc6414 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Sun, Y. et al. Design and fabrication of a shape-morphing soft pneumatic actuator: soft robotic pad. In 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 6214–6220 (IEEE, 2017).

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

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  48. Xu, T., Zhang, J., Salehizadeh, M., Onaizah, O. & Diller, E. Millimeter-scale flexible robots with programmable three-dimensional magnetization and motions. Sci. Robot. 4, eaav4494 (2019).

    Article  PubMed  Google Scholar 

  49. Barnes, M. et al. Reactive 3D printing of shape-programmable liquid crystal elastomer actuators. ACS Appl. Mater. Interfaces 12, 28692–28699 (2020).

    Article  CAS  PubMed  Google Scholar 

  50. Kotikian, A. et al. Untethered soft robotic matter with passive control of shape morphing and propulsion. Sci. Robot. 4, eaax7044 (2019).

    Article  PubMed  Google Scholar 

  51. Boley, J. W. et al. Shape-shifting structured lattices via multimaterial 4D printing. Proc. Natl Acad. Sci. USA 116, 20856–20862 (2019). Three-dimensional multimaterial-printed thermal-induced pattern-to-pattern shape-morphing device assembled by bending lattices with high surface complexity.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  52. Sydney Gladman, A., Matsumoto, E. A., Nuzzo, R. G., Mahadevan, L. & Lewis, J. A. Biomimetic 4D printing. Nat. Mater. 15, 413–418 (2016).

    Article  CAS  PubMed  Google Scholar 

  53. Davidson, Z. S. et al. Monolithic shape-programmable dielectric liquid crystal elastomer actuators. Sci. Adv. 5, eaay0855 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Guo, Y., Zhang, J., Hu, W., Khan, M. T. A. & Sitti, M. Shape-programmable liquid crystal elastomer structures with arbitrary three-dimensional director fields and geometries. Nat. Commun. 12, 5936 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Stanley, A. A. Haptic Jamming: Controllable Mechanical Properties in a Shape-Changing User Interface (Stanford University, 2016).

  56. Klemmer, S. R., Hartmann, B. & Takayama, L. How bodies matter: five themes for interaction design. In Proc. 6th Conference on Designing Interactive systems 140–149 (ACM, 2006).

  57. Urbas, A. M. et al. Roadmap on optical metamaterials. J. Opt. 18, 093005 (2016).

    Article  Google Scholar 

  58. Chen, Y., Ai, B. & Wong, Z. J. Soft optical metamaterials. Nano Converg. 7, 18 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. Cummer, S. A., Christensen, J. & Alù, A. Controlling sound with acoustic metamaterials. Nat. Rev. Mater. 1, 16001 (2016).

    Article  Google Scholar 

  60. Wenz, F. et al. Designing shape morphing behavior through local programming of mechanical metamaterials. Adv. Mater. 33, 2008617 (2021).

    Article  CAS  Google Scholar 

  61. Peng, C. Dynamically Programmable Surfaces for High-Speed Optical Modulation and Detection (Massachusetts Institute of Technology, 2020).

  62. Zhang, Z. & Krushynska, A. Programmable shape-morphing of rose-shaped mechanical metamaterials. APL Mater. https://doi.org/10.1063/5.0099323 (2022).

  63. Liu, C. et al. Programmable mechanical metamaterials: basic concepts, types, construction strategies — a review. Front. Mater. 11, 1361408 (2024).

    Article  Google Scholar 

  64. Hirota, K. & Hirose, M. Surface display: concept and implementation approaches. In Proc. Fifth Int. Conf. Artificial Reality and Tele-Existence 185–192 (ACM-SIGCHI, 1995).

  65. Iwata, H., Yano, H., Nakaizumi, F. & Kawamura, R. Project FEELEX: adding haptic surface to graphics. In Proc. 28th Annual Conference on Computer Graphics and Interactive Techniques 469–476 (ACM, 2001).

  66. Leithinger, D. & Ishii, H. Relief: a scalable actuated shape display. In Proc. Fourth International Conference on Tangible, Embedded, and Embodied Interaction 221–222 (ACM, 2010).

  67. Follmer, S., Leithinger, D., Olwal, A., Hogge, A. & Ishii, H. inFORM: dynamic physical affordances and constraints through shape and object actuation. In Proc. 26th Annual ACM Symposium on User Interface Software and Technology (UIST) 417–426 (ACM, 2013).

  68. Zhu, H. & Book, W. J. Practical structure design and control for digital clay. In ASME International Mechanical Engineering Congress and Exposition 1051–1058 (ASME, 2004).

  69. Deng, Z., Stommel, M. & Xu, W. A novel soft machine table for manipulation of delicate objects inspired by caterpillar locomotion. IEEE/ASME Trans. Mechatron. 21, 1702–1710 (2016).

    Article  Google Scholar 

  70. Poupyrev, I., Nashida, T., Maruyama, S., Rekimoto, J. & Yamaji, Y. Lumen: interactive visual and shape display for calm computing. In ACM SIGGRAPH 2004 Emerging Technologies Vol. 17 (2004).

  71. Wang, T., Zhang, J., Hong, J. & Wang, M. Y. Dielectric elastomer actuators for soft wave-handling systems. Soft Robot. 4, 61–69 (2017).

    Article  PubMed  Google Scholar 

  72. Coelho, M., Ishii, H. & Maes, P. Surflex: a programmable surface for the design of tangible interfaces. In CHI’08 Extended Abstracts on Human Factors in Computing Systems 3429–3434 (2008).

  73. Yang, B. et al. Reprogrammable soft actuation and shape-shifting via tensile jamming. Sci. Adv. 7, eabh2073 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  74. Liu, K., Hacker, F. & Daraio, C. Robotic surfaces with reversible, spatiotemporal control for shape morphing and object manipulation. Sci. Robot. 6, eabf5116 (2021). Programmable shape-morphing device that uses three liquid crystal elastomer bending actuators oriented along each of two orthogonal directions with high load per weight.

    Article  PubMed  Google Scholar 

  75. Bai, Y. et al. A dynamically reprogrammable surface with self-evolving shape morphing. Nature 609, 701–708 (2022). Programmable shape-morphing device driven by the Lorentz force from magnetic fields, comprising 8 × 8 interconnected, serpentine-shaped beams made of thin conductive layers.

    Article  CAS  PubMed  Google Scholar 

  76. Wang, J., Sotzing, M., Lee, M. & Chortos, A. Passively addressed robotic morphing surface (PARMS) based on machine learning. Sci. Adv. 9, eadg8019 (2023). Highly under-actuated programmable shape-morphing device made by 6 × 6 ionic actuator arrays controlled by a machine-learning algorithm.

    Article  PubMed  PubMed Central  Google Scholar 

  77. Stanley, A. A., Hata, K. & Okamura, A. M. Closed-loop shape control of a Haptic Jamming deformable surface. In IEEE Int. Conf. Robotics and Automation (ICRA) 2718–2724 (IEEE, 2016).

  78. Devlin, M. R. et al. Soft, modular, shape-changing displays with hyperelastic bubble arrays. In IEEE/RSJ Int. Conf. Intelligent Robots and Systems (IROS) 5101–5106 (IEEE, 2023).

  79. Rauf, A. M., Bernardo, J. S. & Follmer, S. Electroadhesive auxetics as programmable layer jamming skins for formable crust shape displays. In 2023 IEEE Int. Conf. Robotics and Automation (ICRA) 2591–2597 (IEEE, 2023).

  80. Ni, X. et al. Soft shape-programmable surfaces by fast electromagnetic actuation of liquid metal networks. Nat. Commun. 13, 5576 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  81. Tsimeris, J., Dedman, C., Broughton, M. & Gedeon, T. ForceForm: a dynamically deformable interactive surface. In Proc. 2013 ACM International Conference on Interactive Tabletops and Surfaces 175–178 (ACM, 2013).

  82. Hajiesmaili, E., Larson, N. M., Lewis, J. A. & Clarke, D. R. Programmed shape-morphing into complex target shapes using architected dielectric elastomer actuators. Sci. Adv. 8, eabn9198 (2022).

    Article  PubMed  PubMed Central  Google Scholar 

  83. Shah, D. S., Yang, E. J., Yuen, M. C., Huang, E. C. & Kramer‐Bottiglio, R. Jamming skins that control system rigidity from the surface. Adv. Funct. Mater. 31, 2006915 (2021).

    Article  CAS  Google Scholar 

  84. Pikul, J. H. et al. Stretchable surfaces with programmable 3D texture morphing for synthetic camouflaging skins. Science 358, 210–214 (2017). Pneumatic pattern-to-pattern shape-morphing device based on bulking deformation with fast inverse design and fabrication.

    Article  CAS  PubMed  Google Scholar 

  85. Steltz, E., Mozeika, A., Rodenberg, N., Brown, E. & Jaeger, H. M. JSEL: jamming skin enabled locomotion. In 2009 IEEE/RSJ Int. Conf. Intelligent Robots and Systems 5672–5677 (IEEE, 2009).

  86. Kim, J., Hanna, J. A., Hayward, R. C. & Santangelo, C. D. Thermally responsive rolling of thin gel strips with discrete variations in swelling. Soft Matter 8, 2375–2381 (2012).

    Article  CAS  Google Scholar 

  87. Hauser, A. W., Evans, A. A., Na, J. H. & Hayward, R. C. Photothermally reprogrammable buckling of nanocomposite gel sheets. Angew. Chem. 127, 5524–5527 (2015).

    Article  Google Scholar 

  88. Velazquez, R., Pissaloux, E., Hafez, M. & Szewczyk, J. A low-cost highly-portable tactile display based on shape memory alloy micro-actuators. In IEEE Symp. Virtual Environments, Human–Computer Interfaces and Measurement Systems (IEEE, 2005).

  89. Zhang, J. et al. Robotic artificial muscles: current progress and future perspectives. IEEE Trans. Robot. 35, 761–781 (2019).

    Article  Google Scholar 

  90. Traugutt, N. A. et al. Liquid‐crystal‐elastomer‐based dissipative structures by digital light processing 3D printing. Adv. Mater. 32, 2000797 (2020).

    Article  CAS  Google Scholar 

  91. McConney, M. E. et al. Topography from topology: photoinduced surface features generated in liquid crystal polymer networks. Adv. Mater. 25, 5880–5885 (2013). Photo-activated pattern-to-pattern shape-morphing device with multiple deformation patterns under different light wavelengths based on liquid crystal elastomer networks.

    Article  CAS  PubMed  Google Scholar 

  92. Mac Murray, B. C. et al. Compliant buckled foam actuators and application in patient-specific direct cardiac compression. Soft Robot. 5, 99–108 (2018).

    Article  Google Scholar 

  93. Takei, K. et al. Nanowire active-matrix circuitry for low-voltage macroscale artificial skin. Nat. Mater. 9, 821–826 (2010).

    Article  CAS  PubMed  Google Scholar 

  94. Bao, B., Karnaushenko, D. D., Schmidt, O. G., Song, Y. & Karnaushenko, D. Active matrix flexible sensory systems: materials, design, fabrication, and integration. Adv. Intell. Syst. 4, 2100253 (2022).

    Article  Google Scholar 

  95. Wang, S. et al. Skin electronics from scalable fabrication of an intrinsically stretchable transistor array. Nature 555, 83–88 (2018).

    Article  CAS  PubMed  Google Scholar 

  96. Wang, J. & Chortos, A. Control strategies for soft robot systems. Adv. Intell. Syst. 4, 2100165 (2022).

    Article  Google Scholar 

  97. Laschi, C. & Mazzolai, B. Lessons from animals and plants: the symbiosis of morphological computation and soft robotics. IEEE Robot. Autom. Mag. 23, 107–114 (2016).

    Article  Google Scholar 

  98. Ambrogio, S. et al. Equivalent-accuracy accelerated neural-network training using analogue memory. Nature 558, 60–67 (2018).

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

This work was supported by the Purdue startup funding to A.C. and by NSF award 2301509.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Purdue University, West Lafayette, IN, USA

    Jue Wang & Alex Chortos

Authors
  1. Jue Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alex Chortos
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Both authors researched data for the article and contributed substantially to discussion of the content. J.W. wrote the article. A.C. reviewed and/or edited the manuscript before submission.

Corresponding author

Correspondence to Alex Chortos.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Reviews Materials thanks Rebecca Kramer-Bottiglio and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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

Wang, J., Chortos, A. Performance metrics for shape-morphing devices. Nat Rev Mater 9, 738–751 (2024). https://doi.org/10.1038/s41578-024-00714-w

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41578-024-00714-w

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