Mechanical metamaterial

=== Negative thermal expansion ===

=== Negative thermal expansion ===

These mechanical metamaterials can exhibit coefficients of thermal expansion larger than that of either constituent.{{Cite journal |last1=Lehman |first1=Jeremy |last2=Lakes |first2=Roderic |date=2013-09-01 |title=Stiff lattices with zero thermal expansion and enhanced stiffness via rib cross section optimization |journal=International Journal of Mechanics and Materials in Design |language=en |volume=9 |issue=3 |pages=213–225 |doi=10.1007/s10999-012-9210-x |bibcode=2013IJMMD...9..213L |issn=1573-8841}}{{Cite journal |last1=Zhang |first1=Qiao |last2=Sun |first2=Yuxin |date=2024-01-01 |title=Novel metamaterial structures with negative thermal expansion and tunable mechanical properties |url=https://www.sciencedirect.com/science/article/pii/S0020740323005945 |journal=International Journal of Mechanical Sciences |volume=261 |article-number=108692 |doi=10.1016/j.ijmecsci.2023.108692 |issn=0020-7403|url-access=subscription }}{{Cite journal |last1=Liu |first1=Siyao |last2=Li |first2=Yaning |date=September 2023 |title=Thermal Expansion of Hybrid Chiral Mechanical Metamaterial with Patterned Bi-Strips |journal=Advanced Engineering Materials |language=en |volume=25 |issue=17 |article-number=2300478 |doi=10.1002/adem.202300478 |issn=1438-1656|doi-access=free }} The expansion can be arbitrarily large positive or arbitrarily large negative, or zero. These materials substantially exceed the bounds for thermal expansion of a two-phase composite. They contain considerable void space.

These mechanical metamaterials can exhibit coefficients of thermal expansion larger than that of either constituent.{{Cite journal |last1=Lehman |first1=Jeremy |last2=Lakes |first2=Roderic |date=2013-09-01 |title=Stiff lattices with zero thermal expansion and enhanced stiffness via rib cross section optimization |journal=International Journal of Mechanics and Materials in Design |language=en |volume=9 |issue=3 |pages=213–225 |doi=10.1007/s10999-012-9210-x |bibcode=2013IJMMD...9..213L |issn=1573-8841}}{{Cite journal |last1=Zhang |first1=Qiao |last2=Sun |first2=Yuxin |date=2024-01-01 |title=Novel metamaterial structures with negative thermal expansion and tunable mechanical properties |url=https://www.sciencedirect.com/science/article/pii/S0020740323005945 |journal=International Journal of Mechanical Sciences |volume=261 |article-number=108692 |doi=10.1016/j.ijmecsci.2023.108692 |issn=0020-7403|url-access=subscription }}{{Cite journal |last1=Liu |first1=Siyao |last2=Li |first2=Yaning |date=September 2023 |title=Thermal Expansion of Hybrid Chiral Mechanical Metamaterial with Patterned Bi-Strips |journal=Advanced Engineering Materials |language=en |volume=25 |issue=17 |article-number=2300478 |doi=10.1002/adem.202300478 |issn=1438-1656|doi-access=free }} The expansion can be arbitrarily large positive or arbitrarily large negative, or zero. These materials substantially exceed the bounds for thermal expansion of a two-phase composite. They contain considerable void space.

=== High strength to density ratio ===

=== High strength to density ratio ===

=== Negative bulk modulus ===

=== Negative bulk modulus ===

Mechanical metamaterials with negative effective [[bulk modulus]] exhibit intriguing and counterintuitive properties. Unlike conventional materials that compress under pressure, these materials expand. This anomalous behavior stems from their carefully engineered microstructure, which allows for internal deformation mechanisms that counteract the applied stress. Potential applications for these materials are vast. They could be employed to design [[Acoustic metamaterials|acoustic or phononic metamaterials]],advanced shock absorbers, and energy dissipation systems.{{cite journal |last=Lee |first=Sam Hyeon |author2=Park, Choon Mahn |author3=Seo, Yong Mun |author4=Wang, Zhi Guo |author5=Kim, Chul Koo |date=29 April 2009 |title=Acoustic metamaterial with negative modulus |journal=Journal of Physics: Condensed Matter |volume=21 |issue=17 |article-number=175704 |arxiv=0812.2952 |bibcode=2009JPCM...21q5704L |doi=10.1088/0953-8984/21/17/175704 |pmid=21825432 |s2cid=26358086}}{{cite journal |last=Lee |first=Sam Hyeon |author2=Park, Choon Mahn |author3=Seo, Yong Mun |author4=Wang, Zhi Guo |author5=Kim, Chul Koo |date=1 December 2009 |title=Acoustic metamaterial with negative density |journal=Physics Letters A |volume=373 |issue=48 |pages=4464–4469 |bibcode=2009PhLA..373.4464L |doi=10.1016/j.physleta.2009.10.013}}{{cite journal |last=Yang |first=Z. |author2=Mei, Jun |author3=Yang, Min |author4=Chan, N. |author5=Sheng, Ping |date=1 November 2008 |title=Membrane-Type Acoustic Metamaterial with Negative Dynamic Mass |url=http://repository.ust.hk/ir/bitstream/1783.1-6034/1/PhysRevLett.101.204301.pdf |journal=Physical Review Letters |volume=101 |issue=20 |article-number=204301 |bibcode=2008PhRvL.101t4301Y |doi=10.1103/PhysRevLett.101.204301 |pmid=19113343 |s2cid=714391}}{{cite journal |last=Ding |first=Yiqun |author2=Liu, Zhengyou |author3=Qiu, Chunyin |author4=Shi, Jing |date=August 2007 |title=Metamaterial with Simultaneously Negative Bulk Modulus and Mass Density |journal=Physical Review Letters |volume=99 |issue=9 |article-number=093904 |bibcode=2007PhRvL..99i3904D |doi=10.1103/PhysRevLett.99.093904 |pmid=17931008}}{{cite journal |last=Lee |first=Sam Hyeon |author2=Park, Choon Mahn |author3=Seo, Yong Mun |author4=Wang, Zhi Guo |author5=Kim, Chul Koo |date=1 February 2010 |title=Composite Acoustic Medium with Simultaneously Negative Density and Modulus |journal=Physical Review Letters |volume=104 |issue=5 |article-number=054301 |arxiv=0901.2772 |bibcode=2010PhRvL.104e4301L |doi=10.1103/PhysRevLett.104.054301 |pmid=20366767 |s2cid=119249065}}{{cite journal |last=Li |first=Jensen |author2=Fok, Lee |author3=Yin, Xiaobo |author4=Bartal, Guy |author5=Zhang, Xiang |year=2009 |title=Experimental demonstration of an acoustic magnifying hyperlens |journal=Nature Materials |volume=8 |issue=12 |pages=931–934 |bibcode=2009NatMa...8..931L |doi=10.1038/nmat2561 |pmid=19855382}}{{cite journal |last=Christensen |first=Johan |author2=de Abajo, F. |year=2012 |title=Anisotropic Metamaterials for Full Control of Acoustic Waves |journal=Physical Review Letters |volume=108 |issue=12 |article-number=124301 |bibcode=2012PhRvL.108l4301C |doi=10.1103/PhysRevLett.108.124301 |pmid=22540586 |s2cid=36710766 |hdl-access=free |hdl=10261/92293}}{{cite journal |last=Farhat |first=M. |author2=Enoch, S. |author3=Guenneau, S. |author4=Movchan, A. |year=2008 |title=Broadband Cylindrical Acoustic Cloak for Linear Surface Waves in a Fluid |journal=Physical Review Letters |volume=101 |issue=13 |article-number=134501 |bibcode=2008PhRvL.101m4501F |doi=10.1103/PhysRevLett.101.134501 |pmid=18851453}}{{cite journal |last=Cummer |first=Steven A |author2=Schurig, David |year=2007 |title=One path to acoustic cloaking |journal=New Journal of Physics |volume=9 |issue=3 |page=45 |bibcode=2007NJPh....9...45C |doi=10.1088/1367-2630/9/3/045 |doi-access=free}} Furthermore, their unique elastic properties may find utility in creating novel structural components with enhanced resilience and adaptability to dynamic loads.

Mechanical metamaterials with negative effective [[bulk modulus]] exhibit intriguing and counterintuitive properties. Unlike conventional materials that compress under pressure, these materials expand. This anomalous behavior stems from their carefully engineered microstructure, which allows for internal deformation mechanisms that counteract the applied stress. Potential applications for these materials are vast. They could be employed to design [[Acoustic metamaterials|acoustic or phononic metamaterials]], advanced shock absorbers, and energy dissipation systems.{{cite journal |last=Lee |first=Sam Hyeon |author2=Park, Choon Mahn |author3=Seo, Yong Mun |author4=Wang, Zhi Guo |author5=Kim, Chul Koo |date=29 April 2009 |title=Acoustic metamaterial with negative modulus |journal=Journal of Physics: Condensed Matter |volume=21 |issue=17 |article-number=175704 |arxiv=0812.2952 |bibcode=2009JPCM...21q5704L |doi=10.1088/0953-8984/21/17/175704 |pmid=21825432 |s2cid=26358086}}{{cite journal |last=Lee |first=Sam Hyeon |author2=Park, Choon Mahn |author3=Seo, Yong Mun |author4=Wang, Zhi Guo |author5=Kim, Chul Koo |date=1 December 2009 |title=Acoustic metamaterial with negative density |journal=Physics Letters A |volume=373 |issue=48 |pages=4464–4469 |bibcode=2009PhLA..373.4464L |doi=10.1016/j.physleta.2009.10.013}}{{cite journal |last=Yang |first=Z. |author2=Mei, Jun |author3=Yang, Min |author4=Chan, N. |author5=Sheng, Ping |date=1 November 2008 |title=Membrane-Type Acoustic Metamaterial with Negative Dynamic Mass |url=http://repository.ust.hk/ir/bitstream/1783.1-6034/1/PhysRevLett.101.204301.pdf |journal=Physical Review Letters |volume=101 |issue=20 |article-number=204301 |bibcode=2008PhRvL.101t4301Y |doi=10.1103/PhysRevLett.101.204301 |pmid=19113343 |s2cid=714391}}{{cite journal |last=Ding |first=Yiqun |author2=Liu, Zhengyou |author3=Qiu, Chunyin |author4=Shi, Jing |date=August 2007 |title=Metamaterial with Simultaneously Negative Bulk Modulus and Mass Density |journal=Physical Review Letters |volume=99 |issue=9 |article-number=093904 |bibcode=2007PhRvL..99i3904D |doi=10.1103/PhysRevLett.99.093904 |pmid=17931008}}{{cite journal |last=Lee |first=Sam Hyeon |author2=Park, Choon Mahn |author3=Seo, Yong Mun |author4=Wang, Zhi Guo |author5=Kim, Chul Koo |date=1 February 2010 |title=Composite Acoustic Medium with Simultaneously Negative Density and Modulus |journal=Physical Review Letters |volume=104 |issue=5 |article-number=054301 |arxiv=0901.2772 |bibcode=2010PhRvL.104e4301L |doi=10.1103/PhysRevLett.104.054301 |pmid=20366767 |s2cid=119249065}}{{cite journal |last=Li |first=Jensen |author2=Fok, Lee |author3=Yin, Xiaobo |author4=Bartal, Guy |author5=Zhang, Xiang |year=2009 |title=Experimental demonstration of an acoustic magnifying hyperlens |journal=Nature Materials |volume=8 |issue=12 |pages=931–934 |bibcode=2009NatMa...8..931L |doi=10.1038/nmat2561 |pmid=19855382}}{{cite journal |last=Christensen |first=Johan |author2=de Abajo, F. |year=2012 |title=Anisotropic Metamaterials for Full Control of Acoustic Waves |journal=Physical Review Letters |volume=108 |issue=12 |article-number=124301 |bibcode=2012PhRvL.108l4301C |doi=10.1103/PhysRevLett.108.124301 |pmid=22540586 |s2cid=36710766 |hdl-access=free |hdl=10261/92293}}{{cite journal |last=Farhat |first=M. |author2=Enoch, S. |author3=Guenneau, S. |author4=Movchan, A. |year=2008 |title=Broadband Cylindrical Acoustic Cloak for Linear Surface Waves in a Fluid |journal=Physical Review Letters |volume=101 |issue=13 |article-number=134501 |bibcode=2008PhRvL.101m4501F |doi=10.1103/PhysRevLett.101.134501 |pmid=18851453}}{{cite journal |last=Cummer |first=Steven A |author2=Schurig, David |year=2007 |title=One path to acoustic cloaking |journal=New Journal of Physics |volume=9 |issue=3 |page=45 |bibcode=2007NJPh....9...45C |doi=10.1088/1367-2630/9/3/045 |doi-access=free}} Furthermore, their unique elastic properties may find utility in creating novel structural components with enhanced resilience and adaptability to dynamic loads.

=== Vanishing shear modulus ===

=== Vanishing shear modulus ===

== Active Mechanical Metamaterials ==

== Active Mechanical Metamaterials ==

To date, most mainstream studies on mechanical metamaterials have focused on passive structures with fixed properties, lacking active sensing or feedback capabilities.{{Cite journal |last1=Pishvar |first1=Maya |last2=Harne |first2=Ryan L. |date=2020-08-18 |title=Foundations for Soft, Smart Matter by Active Mechanical Metamaterials |journal=Advanced Science |volume=7 |issue=18 |article-number=2001384 |doi=10.1002/advs.202001384 |pmid=32999844 |issn=2198-3844|pmc=7509744 |bibcode=2020AdvSc...701384P }} Deep integration of advanced functionalities is a critical challenge in exploring the next generation of metamaterials.{{Cite book |url=https://www.nap.edu/catalog/25244 |title=Frontiers of Materials Research: A Decadal Survey |date=2019-08-12 |publisher=National Academies Press |others=Committee on Frontiers of Materials Research: A Decadal Survey, National Materials and Manufacturing Board, Board on Physics and Astronomy, Division on Engineering and Physical Sciences, National Academies of Sciences, Engineering, and Medicine |isbn=978-0-309-48387-2 |location=Washington, D.C.|doi=10.17226/25244 }} Composite mechanical metamaterials could be the key to achieving this goal. However, the entire concept of composite mechanical metamaterials is still in its infancy. Obtaining programmable behavior through the interplay between material and structure in composite mechanical metamaterials enables integrating advanced functionalities into their texture beyond their mechanical properties. The "mechanical metamaterial tree of knowledge" implies that chiral, lattice and negative metamaterials (e.g., negative bulk modulus or negative elastic modulus) are ripe followed by origami and cellular metamaterials.

To date, most mainstream studies on mechanical metamaterials have focused on passive structures with fixed properties, lacking active sensing or feedback capabilities.{{Cite journal |last1=Pishvar |first1=Maya |last2=Harne |first2=Ryan L. |date=2020-08-18 |title=Foundations for Soft, Smart Matter by Active Mechanical Metamaterials |journal=Advanced Science |volume=7 |issue=18 |article-number=2001384 |doi=10.1002/advs.202001384 |pmid=32999844 |issn=2198-3844|pmc=7509744 |bibcode=2020AdvSc...701384P }} Deep integration of advanced functionalities is a critical challenge in exploring the next generation of metamaterials.{{Cite book |url=https://www.nap.edu/catalog/25244 |title=Frontiers of Materials Research: A Decadal Survey |date=2019-08-12 |publisher=National Academies Press |others=Committee on Frontiers of Materials Research: A Decadal Survey, National Materials and Manufacturing Board, Board on Physics and Astronomy, Division on Engineering and Physical Sciences, National Academies of Sciences, Engineering, and Medicine |isbn=978-0-309-48387-2 |location=Washington, D.C.|doi=10.17226/25244 }} Composite mechanical metamaterials could be the key to achieving this goal. However, the entire concept of composite mechanical metamaterials is still in its infancy. Obtaining programmable behavior through the interplay between material and structure in composite mechanical metamaterials enables integrating advanced functionalities into their texture beyond their mechanical properties. The "mechanical metamaterial tree of knowledge" implies that chiral, lattice and negative metamaterials (e.g., negative bulk modulus or negative elastic modulus) are ripe followed by origami and cellular metamaterials.

Recent research trends have been entering a space beyond merely exploring unprecedented mechanical properties. Emerging directions envisioned are sensing, [[energy harvesting]], and actuating mechanical metamaterials.The tree of knowledge reveals that digital computing, digital data storage, and micro/nano-electromechanical systems (MEMS/NEMS) applications are one of the pillars of the mechanical metamaterials future research. Along this direction of evolution, the final target can be active mechanical metamaterials with a level of cognition. Cognitive abilities are crucial elements in a truly "''intelligent mechanical metamaterials''". Similar to complex living organisms, intelligent mechanical metamaterials can potentially deploy their cognitive abilities for sensing, self-powering, and information processing to interact with the surrounding environments, optimizing their response, and creating a sense–decide–respond loop.

Recent research trends have been entering a space beyond merely exploring unprecedented mechanical properties. Emerging directions envisioned are sensing, [[energy harvesting]], and actuating mechanical metamaterials.The tree of knowledge reveals that digital computing, digital data storage, and micro/nano-electromechanical systems (MEMS/NEMS) applications are one of the pillars of the mechanical metamaterials future research. Along this direction of evolution, the final target can be active mechanical metamaterials with a level of cognition. Cognitive abilities are crucial elements in a truly "''intelligent mechanical metamaterials''". Similar to complex living organisms, intelligent mechanical metamaterials can potentially deploy their cognitive abilities for sensing, self-powering, and information processing to interact with the surrounding environments, optimizing their response, and creating a sense–decide–respond loop.

[[File:Mechanical metamaterial tree of knowledge.jpg|thumb|368x368px|Mechanical metamaterial tree of knowledge]]

[[File:Mechanical metamaterial tree of knowledge.jpg|thumb|368x368px|Mechanical metamaterial tree of knowledge]]

=== Programmable mechanical metamaterials ===

=== Programmable mechanical metamaterials ===

=== Responsive mechanical metamaterials ===

=== Responsive mechanical metamaterials ===

Integrating functional materials and mechanical design is an emerging research area to explore responsive mechanical metamaterials. Recent studies explore new classes of mechanical metamaterials that can response to different excitation types such acoustic,{{Cite journal |last1=Li |first1=Feng |last2=Anzel |first2=Paul |last3=Yang |first3=Jinkyu |last4=Kevrekidis |first4=Panayotis G. |last5=Daraio |first5=Chiara |date=2014-10-30 |title=Granular acoustic switches and logic elements |url=https://www.nature.com/articles/ncomms6311 |journal=Nature Communications |language=en |volume=5 |issue=1 |page=5311 |doi=10.1038/ncomms6311 |pmid=25354587 |bibcode=2014NatCo...5.5311L |issn=2041-1723}} thermophotovoltaic{{Cite journal |title=High-efficiency thermophotovoltaic energy conversion enabled by a metamaterial selective emitter |url=https://opg.optica.org/optica/viewmedia.cfm?uri=optica-5-2-213&html=true |access-date=2024-07-23 |journal=Optica |doi=10.1364/optica.5.000213 | date=2018 | last1=Woolf | first1=David N. | last2=Kadlec | first2=Emil A. | last3=Bethke | first3=Don | last4=Grine | first4=Albert D. | last5=Nogan | first5=John J. | last6=Cederberg | first6=Jeffrey G. | last7=Bruce Burckel | first7=D. | last8=Luk | first8=Ting Shan | last9=Shaner | first9=Eric A. | last10=Hensley | first10=Joel M. | volume=5 | issue=2 | page=213 | bibcode=2018Optic...5..213W }} and magnetic.{{Cite journal |last1=Xie |first1=Yunsong |last2=Fan |first2=Xin |last3=Wilson |first3=Jeffrey D. |last4=Simons |first4=Rainee N. |last5=Chen |first5=Yunpeng |last6=Xiao |first6=John Q. |date=2014-09-09 |title=A universal electromagnetic energy conversion adapter based on a metamaterial absorber |journal=Scientific Reports |language=en |volume=4 |issue=1 |page=6301 |doi=10.1038/srep06301 |issn=2045-2322 |pmc=4158331 |pmid=25200005|arxiv=1312.0683 |bibcode=2014NatSR...4.6301X }}

Integrating functional materials and mechanical design is an emerging research area to explore responsive mechanical metamaterials. Recent studies explore new classes of mechanical metamaterials that can response to different excitation types such acoustic,{{Cite journal |last1=Li |first1=Feng |last2=Anzel |first2=Paul |last3=Yang |first3=Jinkyu |last4=Kevrekidis |first4=Panayotis G. |last5=Daraio |first5=Chiara |date=2014-10-30 |title=Granular acoustic switches and logic elements |url=https://www.nature.com/articles/ncomms6311 |journal=Nature Communications |language=en |volume=5 |issue=1 |page=5311 |doi=10.1038/ncomms6311 |pmid=25354587 |bibcode=2014NatCo...5.5311L |issn=2041-1723}} thermophotovoltaic{{Cite journal |title=High-efficiency thermophotovoltaic energy conversion enabled by a metamaterial selective emitter |url=https://opg.optica.org/optica/viewmedia.cfm?uri=optica-5-2-213&html=true |access-date=2024-07-23 |journal=Optica |doi=10.1364/optica.5.000213 | date=2018 | last1=Woolf | first1=David N. | last2=Kadlec | first2=Emil A. | last3=Bethke | first3=Don | last4=Grine | first4=Albert D. | last5=Nogan | first5=John J. | last6=Cederberg | first6=Jeffrey G. | last7=Bruce Burckel | first7=D. | last8=Luk | first8=Ting Shan | last9=Shaner | first9=Eric A. | last10=Hensley | first10=Joel M. | volume=5 | issue=2 | page=213 | bibcode=2018Optic...5..213W }} and magnetic.{{Cite journal |last1=Xie |first1=Yunsong |last2=Fan |first2=Xin |last3=Wilson |first3=Jeffrey D. |last4=Simons |first4=Rainee N. |last5=Chen |first5=Yunpeng |last6=Xiao |first6=John Q. |date=2014-09-09 |title=A universal electromagnetic energy conversion adapter based on a metamaterial absorber |journal=Scientific Reports |language=en |volume=4 |issue=1 |page=6301 |doi=10.1038/srep06301 |issn=2045-2322 |pmc=4158331 |pmid=25200005|arxiv=1312.0683 |bibcode=2014NatSR...4.6301X }}

=== Sensing and energy harvesting mechanical metamaterials ===

=== Sensing and energy harvesting mechanical metamaterials ===