Automated discovery of reprogrammable nonlinear dynamic metamaterials (2024)

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References

  1. Ma, G. & Sheng, P. Acoustic metamaterials: from local resonances to broad horizons. Sci. Adv. 2, e1501595 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  2. Zangeneh-Nejad, F., Sounas, D. L., Alù, A. & Fleury, R. Analogue computing with metamaterials. Nat. Rev. Mater. 6, 207–225 (2021).

    Article  Google Scholar 

  3. Silva, A. et al. Performing mathematical operations with metamaterials. Science 343, 160–163 (2014).

    Article  CAS  PubMed  Google Scholar 

  4. Zhang, S., Xia, C. & Fang, N. Broadband acoustic cloak for ultrasound waves. Phys. Rev. Lett. 106, 024301 (2011).

    Article  PubMed  Google Scholar 

  5. Stenger, N., Wilhelm, M. & Wegener, M. Experiments on elastic cloaking in thin plates. Phys. Rev. Lett. 108, 014301 (2012).

    Article  PubMed  Google Scholar 

  6. Xue, Y. & Zhang, X. Self-adaptive acoustic cloak enabled by soft mechanical metamaterials. Extreme Mech. Lett. 46, 101347 (2021).

    Article  Google Scholar 

  7. Deng, B., Raney, J. R., Bertoldi, K. & Tournat, V. Nonlinear waves in flexible mechanical metamaterials. J. Appl. Phys. 130, 040901 (2021).

    Article  CAS  Google Scholar 

  8. Patil, G. U. & Matlack, K. H. Review of exploiting nonlinearity in phononic materials to enable nonlinear wave responses. Acta Mech. 233, 1–46 (2022).

    Article  Google Scholar 

  9. Nadkarni, N., Arrieta, A. F., Chong, C., Kochmann, D. M. & Daraio, C. Unidirectional transition waves in bistable lattices. Phys. Rev. Lett. 116, 244501 (2016).

    Article  PubMed  Google Scholar 

  10. Raney, J. R. et al. Stable propagation of mechanical signals in soft media using stored elastic energy. Proc. Natl Acad. Sci. USA 113, 9722–9727 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  PubMed  PubMed Central  Google Scholar 

  12. Jin, L. et al. Guided transition waves in multistable mechanical metamaterials. Proc. Natl Acad. Sci. USA 117, 2319–2325 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Zaiser, M. & Zapperi, S. Disordered mechanical metamaterials. Nat. Rev. Phys. 5, 679–688 (2023).

    Article  Google Scholar 

  14. Bendsøe, M. P. & Sigmund, O. Topology Optimization: Theory, Methods, and Applications (Springer, 2004).

  15. Sigmund, O. & Maute, K. Topology optimization approaches. Struct. Multidiscip. Optim. 48, 1031–1055 (2013).

    Article  Google Scholar 

  16. Osanov, M. & Guest, J. K. Topology optimization for architected materials design. Annu. Rev. Mater. Res. 46, 211–233 (2016).

    Article  CAS  Google Scholar 

  17. Wu, J., Sigmund, O. & Groen, J. P. Topology optimization of multi-scale structures: a review. Struct. Multidiscip. Optim. 63, 1455–1480 (2021).

  18. van Dijk, N. P., Maute, K., Langelaar, M. & van Keulen, F. Level-set methods for structural topology optimization: a review. Struct. Multidiscip. Optim. 48, 437–472 (2013).

    Article  Google Scholar 

  19. Sigmund, O. & Jensen, J. S. Systematic design of phononic band-gap materials and structures by topology optimization. Philos. Trans. R. Soc. A 361, 1001–1019 (2003).

    Article  Google Scholar 

  20. Liu, W., Yoon, G. H., Yi, B., Choi, H. & Yang, Y. Controlling wave propagation in one-dimensional structures through topology optimization. Comput. Struct. 241, 106368 (2020).

    Article  Google Scholar 

  21. Dong, H. W., Zhao, S. D., Wang, Y. S. & Zhang, C. Topology optimization of anisotropic broadband double-negative elastic metamaterials. J. Mech. Phys. Solids 105, 54–80 (2017).

    Article  Google Scholar 

  22. Li, Y. F., Meng, F., Zhou, S., Lu, M. H. & Huang, X. Broadband all-angle negative refraction by optimized phononic crystals. Sci. Rep. 7, 7445 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  23. He, J. & Kang, Z. Achieving directional propagation of elastic waves via topology optimization. Ultrasonics 82, 1–10 (2018).

    Article  PubMed  Google Scholar 

  24. Capers, J. Inverse design of thin-plate elastic wave devices. Phys. Rev. Appl. 20, 034064 (2023).

    Article  CAS  Google Scholar 

  25. Bösch, C., Dubček, T., Schindler, F., Fichtner, A. & Serra-Garcia, M. Discovery of topological metamaterials by symmetry relaxation and smooth topological indicators. Phys. Rev. B 102, 241404 (2020).

    Article  Google Scholar 

  26. Jensen, J. S. Topology optimization of dynamics problems with Padé approximants. Int. J. Numer. Methods Eng. 72, 1605–1630 (2007).

    Article  Google Scholar 

  27. Boddeti, N., Tang, Y., Maute, K., Rosen, D. W. & Dunn, M. L. Optimal design and manufacture of variable stiffness laminated continuous fiber reinforced composites. Sci. Rep. 10, 16507 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Wu, K., Sigmund, O. & Du, J. Design of metamaterial mechanisms using robust topology optimization and variable linking scheme. Struct. Multidiscip. Optim. 63, 1975–1988 (2021).

    Article  Google Scholar 

  29. Fraternali, F., Porter, M. A. & Daraio, C. Optimal design of composite granular protectors. Mech. Adv. Mater. Struct. 17, 1–19 (2009).

    Article  Google Scholar 

  30. Oliveri, G. & Overvelde, J. T. Inverse design of mechanical metamaterials that undergo buckling. Adv. Funct. Mater. 30, 1909033 (2020).

    Article  CAS  Google Scholar 

  31. Bessa, M. A., Glowacki, P. & Houlder, M. Bayesian machine learning in metamaterial design: fragile becomes supercompressible. Adv. Mater. 31, 1904845 (2019).

    Article  CAS  Google Scholar 

  32. Mo, C., Perdikaris, P. & Raney, J. R. Accelerated design of architected materials with multifidelity Bayesian optimization. J. Eng. Mech. 149, 04023032 (2023).

    Article  Google Scholar 

  33. Martins, J. R. R. A. & Ning, A. Engineering Design Optimization 1st edn (Cambridge Univ. Press, 2021).

  34. Yang, Z., Yu, C. H. & Buehler, M. J. Deep learning model to predict complex stress and strain fields in hierarchical composites. Sci. Adv. 7, eabd7416 (2021).

    Article  PubMed  PubMed Central  Google Scholar 

  35. Deng, B. et al. Inverse design of mechanical metamaterials with target nonlinear response via a neural accelerated evolution strategy. Adv. Mater. 34, 2206238 (2022).

    Article  CAS  Google Scholar 

  36. Lew, A. J., Jin, K. & Buehler, M. J. Designing architected materials for mechanical compression via simulation, deep learning, and experimentation. npj Comput. Mater. 9, 80 (2023).

    Article  Google Scholar 

  37. Cheng, X. et al. Programming 3D curved mesosurfaces using microlattice designs. Science 379, 1225–1232 (2023).

    Article  CAS  PubMed  Google Scholar 

  38. Silver, D. et al. A general reinforcement learning algorithm that masters chess, shogi, and Go through self-play. Science 362, 1140–1144 (2018).

    Article  CAS  PubMed  Google Scholar 

  39. Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019).

    Article  Google Scholar 

  40. Fawzi, A. et al. Discovering faster matrix multiplication algorithms with reinforcement learning. Nature 610, 47–53 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Baydin, A. G., Pearlmutter, B. A., Radul, A. A. & Siskind, J. M. Automatic differentiation in machine learning: a survey. J. Mach. Learn. Res. 18, 1–43 (2018).

  42. Bradbury, J. et al. JAX: composable transformations of Python+NumPy programs (Google, 2018).

  43. Schoenholz, S. S. & Cubuk, E. D. JAX, M.D.: a framework for differentiable physics. In Proc. 34th International Conference on Neural Information Processing Systems 11428–11441 (Curran Associates, 2020).

  44. Minkov, M. et al. Inverse design of photonic crystals through automatic differentiation. ACS Photon. 7, 1729–1741 (2020).

    Article  CAS  Google Scholar 

  45. Goodrich, C. P., King, E. M., Schoenholz, S. S., Cubuk, E. D. & Brenner, M. P. Designing self-assembling kinetics with differentiable statistical physics models. Proc. Natl Acad. Sci. USA 118, e2024083118 (2021).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. Akerson, A. Optimal structures for failure resistance under impact. J. Mech. Phys. Solids 172, 105172 (2023).

    Article  Google Scholar 

  47. Wang, F. Systematic design of 3D auxetic lattice materials with programmable Poisson’s ratio for finite strains. J. Mech. Phys. Solids 114, 303–318 (2018).

    Article  Google Scholar 

  48. Dou, S., Strachan, B. S., Shaw, S. W. & Jensen, J. S. Structural optimization for nonlinear dynamic response. Philos. Trans. R. Soc. A 373, 20140408 (2015).

    Article  Google Scholar 

  49. Li, L. L. et al. Tailoring the nonlinear response of MEMS resonators using shape optimization. Appl. Phys. Lett. 110, 081902 (2017).

    Article  Google Scholar 

  50. Oktay, D., Mirramezani, M., Medina, E. & Adams, R. P. Neuromechanical autoencoders: learning to couple elastic and neural network nonlinearity. In Proc. International Conference on Learning Representations (ICLR, 2023).

  51. Grima, J. N. & Evans, K. E. Auxetic behavior from rotating squares. J. Mater. Sci. Lett. 19, 1563–1565 (2000).

    Article  CAS  Google Scholar 

  52. Cho, Y. et al. Engineering the shape and structure of materials by fractal cut. Proc. Natl Acad. Sci. USA 111, 17390–17395 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Celli, P. et al. Shape-morphing architected sheets with non-periodic cut patterns. Soft Matter 14, 9744–9749 (2018).

    Article  CAS  PubMed  Google Scholar 

  54. Coulais, C., Kettenis, C. & van Hecke, M. A characteristic length scale causes anomalous size effects and boundary programmability in mechanical metamaterials. Nat. Phys. 14, 40–44 (2018).

    Article  CAS  Google Scholar 

  55. Czajkowski, M., Coulais, C., van Hecke, M. & Rocklin, D. Z. Conformal elasticity of mechanism-based metamaterials. Nat. Commun. 13, 211 (2022).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  56. Zheng, Y., Niloy, I., Tobasco, I., Celli, P. & Plucinsky, P. Modelling planar kirigami metamaterials as generalized elastic continua. Proc. R. Soc. A 479, 20220665 (2023).

    Article  Google Scholar 

  57. Deng, B., Mo, C., Tournat, V., Bertoldi, K. & Raney, J. R. Focusing and mode separation of elastic vector solitons in a 2D soft mechanical metamaterial. Phys. Rev. Lett. 123, 024101 (2019).

    Article  CAS  PubMed  Google Scholar 

  58. Yasuda, H., Korpas, L. M. & Raney, J. R. Transition waves and formation of domain walls in multistable mechanical metamaterials. Phys. Rev. Appl. 13, 054067 (2020).

    Article  CAS  Google Scholar 

  59. Deng, B., Raney, J. R., Tournat, V. & Bertoldi, K. Elastic vector solitons in soft architected materials. Phys. Rev. Lett. 118, 204102 (2017).

    Article  CAS  PubMed  Google Scholar 

  60. Dormand, J. & Prince, P. A family of embedded Runge–Kutta formulae. J. Comput. Appl. Math. 6, 19–26 (1980).

    Article  Google Scholar 

  61. Svanberg, K. The method of moving asymptotes—a new method for structural optimization. Int. J. Numer. Methods Eng. 24, 359–373 (1987).

    Article  Google Scholar 

  62. Johnson, S. G. The NLopt nonlinear-optimization package. GitHub http://github.com/stevengj/nlopt (2007).

  63. Liu, Z. et al. Locally resonant sonic materials. Science 289, 1734–1736 (2000).

    Article  CAS  PubMed  Google Scholar 

  64. Bordiga, G. et al. Automated discovery of reprogrammable nonlinear dynamic metamaterials. Zenodo https://doi.org/10.5281/zenodo.12823471 (2024).

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