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  • Open Access

Remotely tuned metamaterials with emergent elastic properties

Laurin Sartori1,2,*,†, Peer Fischer1,2,3,4, and Athanasios G. Athanassiadis1,2,‡,§

  • *Contact author: l.sartori@amolf.nl
  • †Present address: AMOLF, Amsterdam, The Netherlands.
  • ‡Contact author: thanasi@embl.de
  • §Present address: European Molecular Biology Laboratory, Heidelberg, Germany.

Phys. Rev. Research 8, 043028 – Published 9 October, 2026

DOI: https://doi.org/10.1103/72g7-gqdm

Abstract

We introduce a framework for remotely tunable dynamical metamaterials based on interacting nodes embedded in an elastic matrix, effectively forming meta-atoms governed by a programmable nonlinear landscape. Using secondary acoustic radiation forces between microbubble arrays, we predict and experimentally realize an acoustically actuated linear unit cell exhibiting geometric reconfiguration, discontinuous switching, and memory. Building on these results, we introduce a general numerical model for the system that predicts diverse behaviors in larger lattices, including a remote stiffness softening up to 60% and auxeticity up to ν=−0.22. The theory applies to other modes of actuation (e.g., optical or magnetic) and reveals universal behavior in these systems arising purely from the interplay of local r−n forces and elastic interactions in the lattice.

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References (36)

  1. M. Kadic, G. W. Milton, M. van Hecke, and M. Wegener, 3D metamaterials, Nat. Rev. Phys. 1, 198 (2019).
  2. A. Alù, A. F. Arrieta, E. D. Dottore, M. Dickey, S. Ferracin, R. Harne, H. Hauser, Q. He, J. B. Hopkins, L. P. Hyatt, et al., Roadmap on embodying mechano-intelligence and computing in functional materials and structures, Smart Mater. Struct. 34, 063501 (2025).
  3. C. Coulais, E. Teomy, K. de Reus, Y. Shokef, and M. van Hecke, Combinatorial design of textured mechanical metamaterials, Nature (London) 535, 529 (2016).
  4. L. J. Kwakernaak and M. van Hecke, Counting and sequential information processing in mechanical metamaterials, Phys. Rev. Lett. 130, 268204 (2023).
  5. T. Louvet, P. Omidvar, and M. Serra-Garcia, Reprogrammable, in-materia matrix-vector multiplication with floppy modes, Adv. Intell. Syst. 7, 2500062 (2025).
  6. H. Yasuda, P. R. Buskohl, A. Gillman, T. D. Murphey, S. Stepney, R. A. Vaia, and J. R. Raney, Mechanical computing, Nature (London) 598, 39 (2021).
  7. R. Lakes, Foam structures with a negative Poisson’s ratio, Science 235, 1038 (1987).
  8. A. Lazarus and P. M. Reis, Soft actuation of structured cylinders through auxetic behavior, Adv. Eng. Mater. 17, 815 (2015).
  9. K. K. Dudek, M. Kadic, C. Coulais, and K. Bertoldi, Shape-morphing metamaterials, Nat. Rev. Mater. 10, 783 (2025).
  10. K. Bertoldi, V. Vitelli, J. Christensen, and M. van Hecke, Flexible mechanical metamaterials, Nat. Rev. Mater. 2, 17066 (2017).
  11. R. Galea, K. K. Dudek, P.-S. Farrugia, L. Z. Mangion, J. N. Grima, and R. Gatt, Reconfigurable magneto-mechanical metamaterials guided by magnetic fields, Compos. Struct. 280, 114921 (2022).
  12. L. Du, W. Shi, H. Gao, H. Jia, Q. Zhang, M. Liu, and Y. Xu, Mechanically programmable composite metamaterials with switchable positive/negative Poisson’s ratio, Adv. Funct. Mater. 34, 2314123 (2024).
  13. S. Guillet, A. Poncet, M. Le Blay, W. T. Irvine, V. Vitelli, and D. Bartolo, Melting of nonreciprocal solids: How dislocations propel and fission in flowing crystals, Proc. Natl. Acad. Sci. USA 122, e2412993122 (2025).
  14. M. Caleap and B. W. Drinkwater, Acoustically trapped colloidal crystals that are reconfigurable in real time, Proc. Natl. Acad. Sci. USA 111, 6226 (2014).
  15. R. Fleury, A. B. Khanikaev, and A. Alù, Floquet topological insulators for sound, Nat. Commun. 7, 11744 (2016).
  16. K. A. Forbes, D. S. Bradshaw, and D. L. Andrews, Optical binding of nanoparticles, Nanophotonics 9, 1 (2018).
  17. V. Bjerknes, Fields of Force: Supplementary Lectures, Applications to Meteorology; A Course of Lectures in Mathematical Physics Delivered December 1 to 23, 1905 (Columbia University Press, New York, 1906), Vol. 1.
  18. L. A. Crum, Bjerknes forces on bubbles in a stationary sound field, J. Acoust. Soc. Am. 57, 1363 (1975).
  19. J. Nocedal and S. J. Wright, Line search methods, in Numerical Optimization, edited by T. V. Mikosch, S. I. Resnick, and S. M. Robinson (Springer, New York, NY, 2006), pp. 30–65.
  20. J. Nocedal and S. J. Wright, Sequential quadratic programming, in Numerical Optimization, edited by T. V. Mikosch, S. I. Resnick, and S. M. Robinson (Springer, New York, NY, 2006), pp. 529–562.
  21. L. Sartori, P. Fischer, and A. G. Athanassiadis, Code and data for “Remotely-tuned metamaterials with emergent elastic properties”, [Computer software], Zenodo, 2026, doi: 10.5281/zenodo.19254561.
  22. R. Goyal, A. G. Athanassiadis, Z. Ma, and P. Fischer, Amplification of acoustic forces using microbubble arrays enables manipulation of centimeter-scale objects, Phys. Rev. Lett. 128, 254502 (2022).
  23. T. G. Leighton, The forced bubble, in The Acoustic Bubble (Academic Press, London, 1994), Chap. 4, pp. 287–438.
  24. A. Prosperetti, Thermal effects and damping mechanisms in the forced radial oscillations of gas bubbles in liquids, J. Acoust. Soc. Am. 61, 17 (1977).
  25. M. Lei, W. Hong, Z. Zhao, C. Hamel, M. Chen, H. Lu, and H. J. Qi, 3D printing of auxetic metamaterials with digitally reprogrammable shape, ACS Appl. Mater. Interfaces 11, 22768 (2019).
  26. S. Babaee, J. Shim, J. C. Weaver, E. R. Chen, N. Patel, and K. Bertoldi, 3D soft metamaterials with negative Poisson’s ratio, Adv. Mater. 25, 5044 (2013).
  27. K. Bertoldi, P. M. Reis, S. Willshaw, and T. Mullin, Negative Poisson’s ratio behavior induced by an elastic instability, Adv. Mater. 22, 361 (2010).
  28. B. Wu, B. VanSaders, M. X. Lim, and H. M. Jaeger, Hydrodynamic coupling melts acoustically levitated crystalline rafts, Proc. Natl. Acad. Sci. USA 120, e2301625120 (2023).
  29. B. Wu, E. P. Esposito, Q. Mao, and H. M. Jaeger, Pattern formation in acoustically levitated particle systems with competing near-field interactions, Phys. Rev. Res. 7, 023017 (2025).
  30. M. Kaynak, A. Dolev, and M. S. Sakar, 3D printed acoustically programmable soft microactuators, Soft Rob. 10, 246 (2023).
  31. V. Leroy, M. Devaud, T. Hocquet, and J.-C. Bacri, The bubble cloud as an N-degree of freedom harmonic oscillator, Eur. Phys. J. E 17, 189 (2005).
  32. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, New York, NY, 1999).
  33. M. Lanoy, C. Derec, A. Tourin, and V. Leroy, Manipulating bubbles with secondary Bjerknes forces, Appl. Phys. Lett. 107, 214101 (2015).
  34. G. Regnault, C. Mauger, P. Blanc-Benon, and C. Inserra, Secondary radiation force between two closely spaced acoustic bubbles, Phys. Rev. E 102, 031101(R) (2020).
  35. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, et al., SciPy 1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).
  36. R. G. Budynas and J. K. Nisbett, Shigley’s Mechanical Engineering Design, 8th ed. (McGraw-Hill, New York, 2008).

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