Harnessing plasticity in sequential metamaterials for ideal shock absorption – Nature
Schaedler, T. A. et al. Ultralight metallic microlattices. Science 334, 962–965 (2011).
Google Scholar
Zheng, X. et al. Ultralight, ultrastiff mechanical metamaterials. Science 344, 1373–1377 (2014).
Google Scholar
Meza, L. R., Das, S. & Greer, J. R. Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science 345, 1322–1326 (2014).
Google Scholar
Tancogne-Dejean, T., Spierings, A. B. & Mohr, D. Additively-manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading. Acta Mater. 116, 14–28 (2016).
Google Scholar
Meeussen, A. & van Hecke, M. Multistable sheets with rewritable patterns for switchable shape-morphing. Nature 621, 516–520 (2023).
Google Scholar
Choi, G. P., Dudte, L. H. & Mahadevan, L. Programming shape using kirigami tessellations. Nat. Mater. 18, 999–1004 (2019).
Google Scholar
Gao, T., Bico, J. & Roman, B. Pneumatic cells toward absolute Gaussian morphing. Science 381, 862–867 (2023).
Google Scholar
Coulais, C., Sabbadini, A., Vink, F. & van Hecke, M. Multi-step self-guided pathways for shape-changing metamaterials. Nature 561, 512–515 (2018).
Google Scholar
Florijn, B., Coulais, C. & van Hecke, M. Programmable mechanical metamaterials. Phys. Rev. Lett. 113, 175503 (2014).
Google Scholar
Shan, S. et al. Multistable architected materials for trapping elastic strain energy. Adv. Mater. 27, 4296–4301 (2015).
Google Scholar
Restrepo, D., Mankame, N. D. & Zavattieri, P. D. Phase transforming cellular materials. Extreme Mech. Lett. 4, 52–60 (2015).
Google Scholar
Lakes, R. Foam structures with a negative Poisson’s ratio. Science 235, 1038–1040 (1987).
Google Scholar
Bertoldi, K., Reis, P. M., Willshaw, S. & Mullin, T. Negative Poisson’s ratio behavior induced by an elastic instability. Adv. Mater. 22, 361–366 (2010).
Google Scholar
Babaee, S. et al. 3D soft metamaterials with negative Poisson’s ratio. Adv. Mater. 25, 5044–5049 (2013).
Google Scholar
Jin, L. et al. Guided transition waves in multistable mechanical metamaterials. Proc. Natl Acad. Sci. 117, 2319–2325 (2020).
Google Scholar
Deng, B., Wang, P., He, Q., Tournat, V. & Bertoldi, K. Metamaterials with amplitude gaps for elastic solitons. Nat. Commun. 9, 3410 (2018).
Google Scholar
Bauer, J., Kraus, J. A., Crook, C., Rimoli, J. J. & Valdevit, L. Tensegrity metamaterials: toward failure-resistant engineering systems through delocalized deformation. Adv. Mater. 33, 2005647 (2021).
Google Scholar
Dykstra, D. M., Lenting, C., Masurier, A. & Coulais, C. Buckling metamaterials for extreme vibration damping. Adv. Mater. 35, 2301747 (2023).
Google Scholar
Bertoldi, K., Vitelli, V., Christensen, J. & Van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater. 2, 17066 (2017).
Google Scholar
Jiao, P., Mueller, J., Raney, J. R., Zheng, X. & Alavi, A. H. Mechanical metamaterials and beyond. Nat. Commun. 14, 6004 (2023).
Google Scholar
Djellouli, A. et al. Shell buckling for programmable metafluids. Nature 628, 545–550 (2024).
Google Scholar
Lubbers, L. A., van Hecke, M. & Coulais, C. A nonlinear beam model to describe the postbuckling of wide neo-Hookean beams. J. Mech. Phys. Solids 106, 191–206 (2017).
Google Scholar
Chen, Y. & Jin, L. Reusable energy-absorbing architected materials harnessing snapping-back buckling of wide hyperelastic columns. Adv. Funct. Mater. 31, 2102113 (2021).
Google Scholar
Dykstra, D. M. J., Janbaz, S. & Coulais, C. The extreme mechanics of viscoelastic metamaterials. APL Mater 10, 080702 (2022).
Google Scholar
Bossart, A., Dykstra, D. M., van der Laan, J. & Coulais, C. Oligomodal metamaterials with multifunctional mechanics. Proc. Natl Acad. Sci. 118, e2018610118 (2021).
Google Scholar
Janbaz, S., Narooei, K., van Manen, T. & Zadpoor, A. Strain rate–dependent mechanical metamaterials. Sci. Adv. 6, eaba0616 (2020).
Google Scholar
Janbaz, S. & Coulais, C. Diffusive kinks turn kirigami into machines. Nat. Commun. 15, 1255 (2024).
Google Scholar
Evans, A. G. et al. Concepts for enhanced energy absorption using hollow micro-lattices. Int. J. Impact Eng. 37, 947–959 (2010).
Google Scholar
Rafsanjani, A. & Bertoldi, K. Buckling-induced kirigami. Phys. Rev. Lett. 118, 084301 (2017).
Google Scholar
Zhang, F. et al. Shape morphing of plastic films. Nat. Commun. 13, 7294 (2022).
Google Scholar
Hwang, D., Barron III, E. J., Haque, A. T. & Bartlett, M. D. Shape morphing mechanical metamaterials through reversible plasticity. Sci. Robot. 7, eabg2171 (2022).
Google Scholar
Ren, X., Shen, J., Ghaedizadeh, A., Tian, H. & Xie, Y. M. Experiments and parametric studies on 3D metallic auxetic metamaterials with tuneable mechanical properties. Smart Mater. Struct. 24, 095016 (2015).
Google Scholar
Ghaedizadeh, A., Shen, J., Ren, X. & Xie, Y. M. Tuning the performance of metallic auxetic metamaterials by using buckling and plasticity. Materials 9, 54 (2016).
Google Scholar
Bažant, Z. P. & Cedolin, L. Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories (World Scientific, 2010).
Frenzel, T., Findeisen, C., Kadic, M., Gumbsch, P. & Wegener, M. Tailored buckling microlattices as reusable light-weight shock absorbers. Adv. Mater. 28, 5865–5870 (2016).
Google Scholar
Rafsanjani, A., Jin, L., Deng, B. & Bertoldi, K. Propagation of pop ups in kirigami shells. Proc. Natl Acad. Sci. 116, 8200–8205 (2019).
Google Scholar
Melancon, D., Forte, A. E., Kamp, L. M., Gorissen, B. & Bertoldi, K. Inflatable origami: multimodal deformation via multistability. Adv. Funct. Mater. 32, 2201891 (2022).
Google Scholar
Bense, H. & van Hecke, M. Complex pathways and memory in compressed corrugated sheets. Proc. Natl Acad. Sci. 118, e2111436118 (2021).
Google Scholar
Guo, X., Guzmán, M., Carpentier, D., Bartolo, D. & Coulais, C. Non-orientable order and non-commutative response in frustrated metamaterials. Nature 618, 506–512 (2023).
Google Scholar
Yasuda, H. et al. Mechanical computing. Nature 598, 39–48 (2021).
Google Scholar
Kwakernaak, L. J. & van Hecke, M. Counting and sequential information processing in mechanical metamaterials. Phys. Rev. Lett. 130, 268204 (2023).
Google Scholar
Novelino, L. S., Ze, Q., Wu, S., Paulino, G. H. & Zhao, R. Untethered control of functional origami microrobots with distributed actuation. Proc. Natl Acad. Sci. 117, 24096–24101 (2020).
Google Scholar
Fu, H. et al. Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics. Nat. Mater. 17, 268–276 (2018).
Google Scholar
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).
Google Scholar
Fancher, R. et al. Dependence of the kinetic energy absorption capacity of bistable mechanical metamaterials on impactor mass and velocity. Extreme Mech. Lett. 63, 102044 (2023).
Google Scholar
Overvelde, J. T. B., Shan, S. & Bertoldi, K. Compaction through buckling in 2D periodic, soft and porous structures: effect of pore shape. Adv. Mater. 24, 2337–2342 (2012).
Google Scholar
Overvelde, J. T. & Bertoldi, K. Relating pore shape to the non-linear response of periodic elastomeric structures. J. Mech. Phys. Solids 64, 351–366 (2014).
Google Scholar
van Mastrigt, R., Dijkstra, M., Van Hecke, M. & Coulais, C. Machine learning of implicit combinatorial rules in mechanical metamaterials. Phys. Rev. Lett. 129, 198003 (2022).
Google Scholar
van Mastrigt, R., Coulais, C. & van Hecke, M. Emergent nonlocal combinatorial design rules for multimodal metamaterials. Phys. Rev. E 108, 065002 (2023).
Google Scholar
Deng, F., Nguyen, Q.-K. & Zhang, P. Liquid metal lattice materials with simultaneously high strength and reusable energy absorption. Appl. Mater. Today 29, 101671 (2022).
Google Scholar
Papka, S. D. & Kyriakides, S. Experiments and full-scale numerical simulations of in-plane crushing of a honeycomb. Acta Mater. 46, 2765–2776 (1998).
Google Scholar
Deshpande, V., Ashby, M. & Fleck, N. Foam topology: bending versus stretching dominated architectures. Acta Mater. 49, 1035–1040 (2001).
Google Scholar
Guell Izard, A., Bauer, J., Crook, C., Turlo, V. & Valdevit, L. Ultrahigh energy absorption multifunctional spinodal nanoarchitectures. Small 15, 1903834 (2019).
Google Scholar
Tancogne-Dejean, T. & Mohr, D. Stiffness and specific energy absorption of additively-manufactured metallic BCC metamaterials composed of tapered beams. Int. J. Mech. Sci. 141, 101–116 (2018).
Google Scholar
Rafsanjani, A., Zhang, Y., Liu, B., Rubinstein, S. M. & Bertoldi, K. Kirigami skins make a simple soft actuator crawl. Sci. Robot. 3, eaar7555 (2018).
Google Scholar
Hwang, D., Barron, E. J. III, Haque, A. B. M. T. & Bartlett, M. D. Shape morphing mechanical metamaterials through reversible plasticity. Sci. Robot. 7, eabg2171 (2022).
Google Scholar
Shi, Y. et al. Plasticity-induced origami for assembly of three dimensional metallic structures guided by compressive buckling. Extreme Mech. Lett. 11, 105–110 (2017).
Google Scholar
Stern, M., Pinson, M. B. & Murugan, A. Continual learning of multiple memories in mechanical networks. Phys. Rev. X 10, 031044 (2020).
Google Scholar
Pashine, N., Hexner, D., Liu, A. J. & Nagel, S. R. Directed aging, memory, and nature’s greed. Sci. Adv. 5, eaax4215 (2019).
Google Scholar
Euler, L. Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes, Sive Solutio Problematis Isoperimetrici Latissimo Sensu Accepti Vol. 1 (Springer, 1952).
Shanley, F. R. Inelastic column theory. J. Aeronaut. Sci. 14, 261–268 (1947).
Google Scholar
Hutchinson, J. W. Plastic buckling. Adv. Appl. Mech. 14, 67–144 (1974).
Google Scholar
Cimetière, A., Leger, A. & Pratt, E. On the coupling of large deformations and elastic-plasticity in the mechanics of a simple system. J. Mech. Phys. Solids 128, 239–254 (2019).
Google Scholar
Liu, W. Leveraging plasticity to design sequential metamaterials with ideal shock absorption. Zenodo https://doi.org/10.5281/zenodo.10074741 (2024).
Resch, R. D. Geometrical device having articulated relatively movable sections. US patent 3,201,894 (1965).
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).
Google Scholar
Czajkowski, M., Coulais, C., van Hecke, M. & Rocklin, D. Conformal elasticity of mechanism-based metamaterials. Nat. Commun. 13, 211 (2022).
Google Scholar