Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Xiu, Haning; Frankel, Ian; Liu, Harry; Qian, Kai; Sarkar, Siddhartha; MacNider, Brianna; Chen, Zi; Boechler, Nicholas; Mao, Xiaoming

doi:10.1073/pnas.2217928120

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Journal Article · Mon Apr 24 00:00:00 EDT 2023 · Proceedings of the National Academy of Sciences of the United States of America

DOI:https://doi.org/10.1073/pnas.2217928120· OSTI ID:1971269

^[1]; ^[2]; ^[3]; ^[2]; Sarkar, Siddhartha ^[3]; ^[2]; ^[4]; Boechler, Nicholas ^[2]; Mao, Xiaoming ^[3]

Department of Surgery, Brigham and Women’s Hospital/Harvard Medical School, Boston, MA 02115, Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093
Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA 92093
Department of Physics, University of Michigan, Ann Arbor, MI 48109
Department of Surgery, Brigham and Women’s Hospital/Harvard Medical School, Boston, MA 02115

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

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Research Organization:: Krell Institute, Ames, IA (United States)

Sponsoring Organization:: US Army Research Office (ARO); US Department of the Navy, Office of Naval Research (ONR); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003960

OSTI ID:: 1971269

Alternate ID(s):: OSTI ID: 2417936

Journal Information:: Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 18 Vol. 120; ISSN 0027-8424

Publisher:: Proceedings of the National Academy of SciencesCopyright Statement

Country of Publication:: United States

Language:: English

References (68)

Topological Materials for Functional Optoelectronic Devices Chorsi, Hamid; Cheng, Bing; Zhao, Bo Advanced Functional Materials, Vol. 32, Issue 19 https://doi.org/10.1002/adfm.202110655	journal	March 2022
Intrinsically Polar Elastic Metamaterials Bilal, Osama R.; Süsstrunk, Roman; Daraio, Chiara Advanced Materials, Vol. 29, Issue 26 https://doi.org/10.1002/adma.201700540	journal	May 2017
Review of exploiting nonlinearity in phononic materials to enable nonlinear wave responses Patil, Ganesh U.; Matlack, Kathryn H. Acta Mechanica, Vol. 233, Issue 1 https://doi.org/10.1007/s00707-021-03089-z	journal	November 2021
Buckminster Fuller's “Tensegrity” structures and Clerk Maxwell's rules for the construction of stiff frames Calladine, C. R. International Journal of Solids and Structures, Vol. 14, Issue 2 https://doi.org/10.1016/0020-7683(78)90052-5	journal	January 1978
On the determinacy of repetitive structures Guest, S. Journal of the Mechanics and Physics of Solids, Vol. 51, Issue 3 https://doi.org/10.1016/S0022-5096(02)00107-2	journal	March 2003
An underwater metamaterial for broadband acoustic absorption at low frequency Gao, Nansha; Lu, Kuan Applied Acoustics, Vol. 169 https://doi.org/10.1016/j.apacoust.2020.107500	journal	December 2020
Topological mechanical metamaterials: A brief review Xin, Li; Siyuan, Yu; Harry, Liu Current Opinion in Solid State and Materials Science, Vol. 24, Issue 5 https://doi.org/10.1016/j.cossms.2020.100853	journal	October 2020
Soft topological lattice wheels Zunker, William; Gonella, Stefano Extreme Mechanics Letters, Vol. 46 https://doi.org/10.1016/j.eml.2021.101344	journal	July 2021
Reciprocity in reflection and transmission: What is a ‘phonon diode’? Maznev, A. A.; Every, A. G.; Wright, O. B. Wave Motion, Vol. 50, Issue 4 https://doi.org/10.1016/j.wavemoti.2013.02.006	journal	June 2013
Multiphoton Nanosculpting of Optical Resonant and Nonresonant Microsensors on Fiber Tips Williams, Jeremiah C.; Chandrahalim, Hengky; Suelzer, Joseph S. ACS Applied Materials & Interfaces, Vol. 14, Issue 17 https://doi.org/10.1021/acsami.2c01033	journal	April 2022
Flexible mechanical metamaterials Bertoldi, Katia; Vitelli, Vincenzo; Christensen, Johan Nature Reviews Materials, Vol. 2, Issue 11 https://doi.org/10.1038/natrevmats.2017.66	journal	October 2017
Transformable topological mechanical metamaterials Rocklin, D. Zeb; Zhou, Shangnan; Sun, Kai Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms14201	journal	January 2017
Non-reciprocal and highly nonlinear active acoustic metamaterials Popa, Bogdan-Ioan; Cummer, Steven A. Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms4398	journal	February 2014
Topological solitons as addressable phase bits in a driven laser Garbin, Bruno; Javaloyes, Julien; Tissoni, Giovanna Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms6915	journal	January 2015
Origami structures with a critical transition to bistability arising from hidden degrees of freedom Silverberg, Jesse L.; Na, Jun-Hee; Evans, Arthur A. Nature Materials, Vol. 14, Issue 4 https://doi.org/10.1038/nmat4232	journal	March 2015
Topological boundary modes in isostatic lattices Kane, C. L.; Lubensky, T. C. Nature Physics, Vol. 10, Issue 1 https://doi.org/10.1038/nphys2835	journal	December 2013
Topological modes bound to dislocations in mechanical metamaterials Paulose, Jayson; Chen, Bryan Gin-ge; Vitelli, Vincenzo Nature Physics, Vol. 11, Issue 2 https://doi.org/10.1038/nphys3185	journal	January 2015
A road to reality with topological superconductors Beenakker, Carlo; Kouwenhoven, Leo Nature Physics, Vol. 12, Issue 7 https://doi.org/10.1038/nphys3778	journal	June 2016
Topological mechanics Huber, Sebastian D. Nature Physics, Vol. 12, Issue 7 https://doi.org/10.1038/nphys3801	journal	June 2016
Non-Hermitian physics and PT symmetry El-Ganainy, Ramy; Makris, Konstantinos G.; Khajavikhan, Mercedeh Nature Physics, Vol. 14, Issue 1 https://doi.org/10.1038/nphys4323	journal	January 2018
Ultrafast optical circuit switching for data centers using integrated soliton microcombs Raja, Arslan Sajid; Lange, Sophie; Karpov, Maxim Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-25841-8	journal	October 2021
Conformal elasticity of mechanism-based metamaterials Czajkowski, Michael; Coulais, Corentin; van Hecke, Martin Nature Communications, Vol. 13, Issue 1 https://doi.org/10.1038/s41467-021-27825-0	journal	January 2022
Non-reciprocal photonics based on time modulation Sounas, Dimitrios L.; Alù, Andrea Nature Photonics, Vol. 11, Issue 12 https://doi.org/10.1038/s41566-017-0051-x	journal	November 2017
Gap solitons in a one-dimensional driven-dissipative topological lattice Pernet, Nicolas; St-Jean, Philippe; Solnyshkov, Dmitry D. Nature Physics, Vol. 18, Issue 6 https://doi.org/10.1038/s41567-022-01599-8	journal	May 2022
The role of polymer mechanochemistry in responsive materials and additive manufacturing Ghanem, Maroun Abi; Basu, Amrita; Behrou, Reza Nature Reviews Materials, Vol. 6, Issue 1 https://doi.org/10.1038/s41578-020-00249-w	journal	October 2020
Topological electronics Gilbert, Matthew J. Communications Physics, Vol. 4, Issue 1 https://doi.org/10.1038/s42005-021-00569-5	journal	April 2021
Physics for neuromorphic computing Marković, Danijela; Mizrahi, Alice; Querlioz, Damien Nature Reviews Physics, Vol. 2, Issue 9 https://doi.org/10.1038/s42254-020-0208-2	journal	July 2020
Soluble Model for Fibrous Structures with Steric Constraints Gennes, P. -G. de The Journal of Chemical Physics, Vol. 48, Issue 5 https://doi.org/10.1063/1.1669420	journal	March 1968
Nonlinear topological photonics Smirnova, Daria; Leykam, Daniel; Chong, Yidong Applied Physics Reviews, Vol. 7, Issue 2 https://doi.org/10.1063/1.5142397	journal	June 2020
Surface phonons, elastic response, and conformal invariance in twisted kagome lattices Sun, K.; Souslov, A.; Mao, X. Proceedings of the National Academy of Sciences, Vol. 109, Issue 31 https://doi.org/10.1073/pnas.1119941109	journal	June 2012
Nonlinear conduction via solitons in a topological mechanical insulator Chen, B. G. -g.; Upadhyaya, N.; Vitelli, V. Proceedings of the National Academy of Sciences, Vol. 111, Issue 36 https://doi.org/10.1073/pnas.1405969111	journal	August 2014
Hidden symmetries generate rigid folding mechanisms in periodic origami McInerney, James; Chen, Bryan Gin-ge; Theran, Louis Proceedings of the National Academy of Sciences, Vol. 117, Issue 48 https://doi.org/10.1073/pnas.2005089117	journal	November 2020
Oligomodal metamaterials with multifunctional mechanics Bossart, Aleksi; Dykstra, David M. J.; van der Laan, Jop Proceedings of the National Academy of Sciences, Vol. 118, Issue 21 https://doi.org/10.1073/pnas.2018610118	journal	May 2021
Non-Hermitian physics Ashida, Yuto; Gong, Zongping; Ueda, Masahito Advances in Physics, Vol. 69, Issue 3 https://doi.org/10.1080/00018732.2021.1876991	journal	July 2020
Optical spatial solitons: historical overview and recent advances Chen, Zhigang; Segev, Mordechai; Christodoulides, Demetrios N. Reports on Progress in Physics, Vol. 75, Issue 8 https://doi.org/10.1088/0034-4885/75/8/086401	journal	July 2012
Phonons and elasticity in critically coordinated lattices Lubensky, T. C.; Kane, C. L.; Mao, Xiaoming Reports on Progress in Physics, Vol. 78, Issue 7 https://doi.org/10.1088/0034-4885/78/7/073901	journal	June 2015
Nonlinear coherent structures in granular crystals Chong, C.; Porter, Mason A.; Kevrekidis, P. G. Journal of Physics: Condensed Matter, Vol. 29, Issue 41 https://doi.org/10.1088/1361-648X/aa7672	journal	September 2017
Directional mechanical response in the bulk of topological metamaterials Rocklin, D. Zeb New Journal of Physics, Vol. 19, Issue 6 https://doi.org/10.1088/1367-2630/aa7155	journal	June 2017
Fracturing of topological Maxwell lattices Zhang, Leyou; Mao, Xiaoming New Journal of Physics, Vol. 20, Issue 6 https://doi.org/10.1088/1367-2630/aac765	journal	June 2018
Experimental observation of topological phase transitions in a mechanical 1D-SSH model Thatcher, Luke; Fairfield, Parker; Merlo-Ramírez, Lázaro Physica Scripta, Vol. 97, Issue 3 https://doi.org/10.1088/1402-4896/ac4ed2	journal	February 2022
Modelling planar kirigami metamaterials as generalized elastic continua Zheng, Y.; Niloy, I.; Tobasco, I. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 479, Issue 2272 https://doi.org/10.1098/rspa.2022.0665	journal	April 2023
Switchable phonon diodes using nonlinear topological Maxwell lattices Zhou, Di; Ma, Jihong; Sun, Kai Physical Review B, Vol. 101, Issue 10 https://doi.org/10.1103/PhysRevB.101.104106	journal	March 2020
Majorana-based quantum computing in nanowire devices Tutschku, C.; Reinthaler, R. W.; Lei, C. Physical Review B, Vol. 102, Issue 12 https://doi.org/10.1103/PhysRevB.102.125407	journal	September 2020
Stability of topological edge states under strong nonlinear effects Chaunsali, Rajesh; Xu, Haitao; Yang, Jinkyu Physical Review B, Vol. 103, Issue 2 https://doi.org/10.1103/PhysRevB.103.024106	journal	January 2021
Topological protection in a strongly nonlinear interface lattice Tempelman, Joshua R.; Matlack, Kathryn H.; Vakakis, Alexander F. Physical Review B, Vol. 104, Issue 17 https://doi.org/10.1103/PhysRevB.104.174306	journal	November 2021
Nonlinear topological edge states: From dynamic delocalization to thermalization Many Manda, Bertin; Chaunsali, Rajesh; Theocharis, Georgios Physical Review B, Vol. 105, Issue 10 https://doi.org/10.1103/PhysRevB.105.104308	journal	March 2022
Nonlinear mechanics of thin frames Moshe, Michael; Esposito, Edward; Shankar, Suraj Physical Review E, Vol. 99, Issue 1 https://doi.org/10.1103/PhysRevE.99.013002	journal	January 2019
Quantum Time Crystals Wilczek, Frank Physical Review Letters, Vol. 109, Issue 16 https://doi.org/10.1103/PhysRevLett.109.160401	journal	October 2012
Topological Acoustics Yang, Zhaoju; Gao, Fei; Shi, Xihang Physical Review Letters, Vol. 114, Issue 11 https://doi.org/10.1103/PhysRevLett.114.114301	journal	March 2015
Design of Pseudo-Mechanisms and Multistable Units for Mechanical Metamaterials Singh, Nitin; van Hecke, Martin Physical Review Letters, Vol. 126, Issue 24 https://doi.org/10.1103/PhysRevLett.126.248002	journal	June 2021
Topology in Nonlinear Mechanical Systems Lo, Po-Wei; Santangelo, Christian D.; Chen, Bryan Gin-ge Physical Review Letters, Vol. 127, Issue 7 https://doi.org/10.1103/PhysRevLett.127.076802	journal	August 2021
Continuum Field Theory for the Deformations of Planar Kirigami Zheng, Yue; Niloy, Imtiar; Celli, Paolo Physical Review Letters, Vol. 128, Issue 20 https://doi.org/10.1103/PhysRevLett.128.208003	journal	May 2022
Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States Zabusky, N. J.; Kruskal, M. D. Physical Review Letters, Vol. 15, Issue 6 https://doi.org/10.1103/PhysRevLett.15.240	journal	August 1965
Solitons in Polyacetylene Su, W. P.; Schrieffer, J. R.; Heeger, A. J. Physical Review Letters, Vol. 42, Issue 25 https://doi.org/10.1103/PhysRevLett.42.1698	journal	June 1979
Pattern formation outside of equilibrium Cross, M. C.; Hohenberg, P. C. Reviews of Modern Physics, Vol. 65, Issue 3 https://doi.org/10.1103/RevModPhys.65.851	journal	July 1993
Continuous quantum phase transitions Sondhi, S. L.; Girvin, S. M.; Carini, J. P. Reviews of Modern Physics, Vol. 69, Issue 1 https://doi.org/10.1103/RevModPhys.69.315	journal	January 1997
Colloquium: Topological insulators Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067 https://doi.org/10.1103/RevModPhys.82.3045	journal	November 2010
Topological insulators and superconductors Qi, Xiao-Liang; Zhang, Shou-Cheng Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1057	journal	October 2011
Colloquium : Nonlinear metamaterials Lapine, Mikhail; Shadrivov, Ilya V.; Kivshar, Yuri S. Reviews of Modern Physics, Vol. 86, Issue 3 https://doi.org/10.1103/RevModPhys.86.1093	journal	September 2014
Space-time duality and the theory of temporal imaging Kolner, B. H. IEEE Journal of Quantum Electronics, Vol. 30, Issue 8 https://doi.org/10.1109/3.301659	journal	January 1994
Symplectic Analysis of Wrinkles in Elastic Layers With Graded Stiffnesses Sui, Jianjun; Chen, Junbo; Zhang, Xiaoxiao Journal of Applied Mechanics, Vol. 86, Issue 1 https://doi.org/10.1115/1.4041620	journal	October 2018
Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation Zhang, Hang; Wu, Jun; Fang, Daining Science Advances, Vol. 7, Issue 9 https://doi.org/10.1126/sciadv.abf1966	journal	February 2021
Optical Spatial Solitons and Their Interactions: Universality and Diversity Stegeman, G. I. Science, Vol. 286, Issue 5444 https://doi.org/10.1126/science.286.5444.1518	journal	November 1999
Dissipative Kerr solitons in optical microresonators Kippenberg, Tobias J.; Gaeta, Alexander L.; Lipson, Michal Science, Vol. 361, Issue 6402 https://doi.org/10.1126/science.aan8083	journal	August 2018
Nonlinear tuning of PT symmetry and non-Hermitian topological states Xia, Shiqi; Kaltsas, Dimitrios; Song, Daohong Science, Vol. 372, Issue 6537 https://doi.org/10.1126/science.abf6873	journal	April 2021
Maxwell Lattices and Topological Mechanics Mao, Xiaoming; Lubensky, Tom C. Annual Review of Condensed Matter Physics, Vol. 9, Issue 1 https://doi.org/10.1146/annurev-conmatphys-033117-054235	journal	March 2018
Nonlinear Dynamics and Chaos Strogatz, Steven H. https://doi.org/10.1201/9780429492563	book	January 2015
Topological wave insulators: a review Zangeneh-Nejad, Farzad; Alù, Andrea; Fleury, Romain Comptes Rendus. Physique, Vol. 21, Issue 4-5 https://doi.org/10.5802/crphys.3	journal	December 2020

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36 MATERIALS SCIENCE
engineering
mechanics
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non-Hermitian
nonlinearity
physical sciences
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Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

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