A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility
Abstract
:1. Introduction
2. Materials and Methods
2.1. The System Studied
2.2. Analytical Model
- The stiffness is the result of changes in the angles θ between the squares with the out-of-plane elements being connected through pin-joints which offer no resistance.
- The stiffness is the result of changes in the out-of-plane angles ϕ between the ligaments with the squares being connected though frictionless hinges.
- Both the in-plane and out-of-plane hinges associated with the angles θ and ϕ offer resistance.
2.2.1. The Poisson’s Ratios
2.2.2. The Young’s Moduli
2.2.3. The Compliance Matrix, Linear Compressibility, and Off-Axis Properties
3. Results and Discussion
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
References
- Callister, W.D.; Rethwisch, D.G. Materials Science and Engineering: An Introduction, 9th ed.; John Wiley & Sons: Hoboken, NJ, USA, 2007; ISBN 9780471736967. [Google Scholar]
- Evans, K.E.; Nkansah, M.A.; Hutcherson, I.J.; Rogers, S.C. Molecular network design. Nature 1991, 353, 124. [Google Scholar] [CrossRef]
- Baughman, R.H.; Stafström, S.; Cui, C.; Dantas, S.O. Materials with negative compressibilities in one or more dimensions. Sciences 1998, 279, 1522–1524. [Google Scholar] [CrossRef] [PubMed]
- Grima, J.N.; Chetcuti, E.; Manicaro, E.; Attard, D.; Camilleri, M.; Gatt, R.; Evans, K.E. On the auxetic properties of generic rotating rigid triangles. Proc. R. Soc. A Math. Phys. Eng. Sci. 2012, 468, 810–830. [Google Scholar] [CrossRef]
- Chekkal, I.; Remillat, C.; Scarpa, F. Acoustic properties of auxetic foams. In Proceedings of the WIT Transactions on the Built Environment, New Forest, UK, 19–21 June 2012. [Google Scholar]
- Duncan, O.; Shepherd, T.; Moroney, C.; Foster, L.; Venkatraman, P.; Winwood, K.; Allen, T.; Alderson, A. Review of Auxetic Materials for Sports Applications: Expanding Options in Comfort and Protection. Appl. Sci. 2018, 8, 941. [Google Scholar] [CrossRef] [Green Version]
- Evans, K.E.; Alderson, K.L. Auxetic materials: The positive side of being negative. Eng. Sci. Educ. 2000, 9, 148–154. [Google Scholar] [CrossRef]
- Dudek, M.R.; Wojciechowski, K.W.; Grima, J.N.; Caruana-Gauci, R.; Dudek, K.K. Colossal magnetocaloric effect in magneto-auxetic systems. Smart Mater. Struct. 2015, 24, 085027. [Google Scholar] [CrossRef] [Green Version]
- Grima-Cornish, J.N. Auxetics: Don’t Pull Me, I’ll Get Fatter! IUCr Newsl. 2019, 27. Available online: https://www.iucr.org/news/newsletter/volume-27/number-2/auxetics (accessed on 23 November 2019).
- Cairns, A.B.; Goodwin, A.L. Negative linear compressibility. Phys. Chem. Chem. Phys. 2015, 17, 20449–20465. [Google Scholar] [CrossRef] [Green Version]
- Grima, J.N.; Jackson, R.; Alderson, A.; Evans, K.E. Do zeolites have negative Poisson’s ratios? Adv. Mater. 2000, 12, 1912–1918. [Google Scholar] [CrossRef]
- Grima, J.N.; Alderson, A.; Evans, K.E. Zeolites with negative Poisson’s ratios. Presented at the 4th Materials Chemistry Conference, Dublin, Ireland, July 1999; p. 81. [Google Scholar]
- Sanchez-Valle, C.; Sinogeikin, S.V.; Lethbridge, Z.A.D.; Walton, R.I.; Smith, C.W.; Evans, K.E.; Bass, J.D. Brillouin scattering study on the single-crystal elastic properties of natrolite and analcime zeolites. J. Appl. Phys. 2005, 98, 053508. [Google Scholar] [CrossRef] [Green Version]
- Grima, J.N.; Gatt, R.; Zammit, V.; Williams, J.J.; Evans, K.E.; Alderson, A.; Walton, R.I. Natrolite: A zeolite with negative Poisson’s ratios. J. Appl. Phys. 2007, 101, 086102. [Google Scholar] [CrossRef]
- Alderson, A.; Evans, K.E. Deformation mechanisms leading to auxetic behaviour in the alpha-cristobalite and alpha-quartz structures of both silica and germania. J. Phys. Condens. Matter 2009, 21, 025401. [Google Scholar] [CrossRef] [Green Version]
- He, C.; Liu, P.; Griffin, A.C. Toward Negative Poisson Ratio Polymers through Molecular Design. Macromolecules 1998, 31, 3145–3147. [Google Scholar] [CrossRef]
- Boba, K.; Bianchi, M.; McCombe, G.; Gatt, R.; Griffin, A.C.; Richardson, R.M.; Scarpa, F.; Hamerton, I.; Grima, J.N. Blocked Shape Memory Effect in Negative Poisson’s Ratio Polymer Metamaterials. ACS Appl. Mater. Interfaces 2016, 8, 20319–20328. [Google Scholar] [CrossRef] [PubMed]
- Grima-Cornish, J.N.; Grima, J.N.; Evans, K.E. On the Structural and Mechanical Properties of Poly(Phenylacetylene) Truss-Like Hexagonal Hierarchical Nanonetworks. Phys. Status Solidi B 2017, 254, 1700190. [Google Scholar] [CrossRef]
- Degabriele, E.P.; Grima-Cornish, J.N.; Attard, D.; Caruana-Gauci, R.; Gatt, R.; Evans, K.E.; Grima, J.N. On the Mechanical Properties of Graphyne, Graphdiyne, and Other Poly(Phenylacetylene) Networks. Phys. Status Solidi B 2017, 254, 1700380. [Google Scholar] [CrossRef]
- Grima, J.N.; Evans, K.E. Self expanding molecular networks. Chem. Commun. 2000, 15, 1531–1532. [Google Scholar] [CrossRef]
- Suzuki, Y.; Cardone, G.; Restrepo, D.; Zavattieri, P.D.; Baker, T.S.; Tezcan, F.A. Self-assembly of coherently dynamic, auxetic, two-dimensional protein crystals. Nature 2016, 533, 369–373. [Google Scholar] [CrossRef]
- Evans, K.E.; Alderson, A.; Christian, F.R. Auxetic two-dimensional polymer networks. An example of tailoring geometry for specific mechanical properties. J. Chem. Soc. Faraday Trans. 1995, 91, 2671–2680. [Google Scholar] [CrossRef]
- Goodwin, A.L.; Keen, D.A.; Tucker, M.G. Large negative linear compressibility of Ag3[Co(CN)6]. Proc. Natl. Acad. Sci. USA 2008, 105, 18708–18713. [Google Scholar] [CrossRef] [Green Version]
- Li, W.; Probert, M.R.; Kosa, M.; Bennett, T.D.; Thirumurugan, A.; Burwood, R.P.; Parinello, M.; Howard, J.A.K.; Cheetham, A.K. Negative Linear Compressibility of a Metal–Organic Framework. J. Am. Chem. Soc. 2012, 134, 11940–11943. [Google Scholar] [CrossRef] [PubMed]
- Collings, I.E.; Goodwin, A.L. Metal–organic frameworks under pressure. J. Appl. Phys. 2019, 126, 181101. [Google Scholar] [CrossRef] [Green Version]
- Grima, J.N.; Evans, K.E. Auxetic behavior from rotating squares. J. Mater. Sci. Lett. 2000, 19, 1563–1565. [Google Scholar] [CrossRef]
- Grima, J.N.; Alderson, A.; Evans, K.E. Auxetic behaviour from rotating rigid units. Phys. Status Solidi B 2005, 242, 561–575. [Google Scholar] [CrossRef]
- Grima, J.N.; Gatt, R.; Alderson, A.; Evans, K.E. On the Auxetic Properties of ‘Rotating Rectangles’ with Different Connectivity. J. Phys. Soc. Jpn. 2005, 74, 2866–2867. [Google Scholar] [CrossRef]
- Grima, J.N.; Farrugia, P.S.; Gatt, R.; Attard, D. On the auxetic properties of rotating rhombi and parallelograms: A preliminary investigation. Phys. Status Solidi B 2008, 245, 521–529. [Google Scholar] [CrossRef]
- Attard, D.; Manicaro, E.; Grima, J.N. On rotating rigid parallelograms and their potential for exhibiting auxetic behaviour. Phys. Status Solidi B 2009, 246, 2033–2044. [Google Scholar] [CrossRef]
- Dudek, K.K.; Attard, D.; Caruana-Gauci, R.; Wojciechowski, K.W.; Grima, J.N. Unimode metamaterials exhibiting negative linear compressibility and negative thermal expansion. Smart Mater. Struct. 2016, 25, 025009. [Google Scholar] [CrossRef]
- Attard, D.; Caruana-Gauci, R.; Gatt, R.; Grima, J.N. Negative linear compressibility from rotating rigid units. Phys. Status Solidi B 2016, 253, 1410–1418. [Google Scholar] [CrossRef]
- Baughman, R.H.; Shacklette, J.M.; Zakhidov, A.A.; Stafströ, S. Negative Poisson’s ratios as a common feature of cubic metals. Nature 1998, 392, 362–365. [Google Scholar] [CrossRef]
- Grima, J.N.; Williams, J.J.; Evans, K.E. Networked calix[4]arene polymers with unusual mechanical properties. Chem. Commun. 2005, 32, 4065–4067. [Google Scholar] [CrossRef] [PubMed]
- Almgren, F. An isotropic three-dimensional structure with Poisson’s ratio =−1. J. Elast. 1985, 15, 427–430. [Google Scholar]
- Gibson, L.J.; Ashby, M.F.; Schajer, G.S.; Robertson, G. The Mechanics of two-dimensional cellular materials. Proc. R. Soc. Lond. A 1982, 382, 25–42. [Google Scholar] [CrossRef]
- Masters, I.G.; Evans, K.E. Models for the elastic deformation of honeycombs. Compos. Struct. 1996, 35, 403–422. [Google Scholar] [CrossRef]
- Grima, J.N.; Attard, D.; Caruana-Gauci, R.; Gatt, R. Negative linear compressibility of hexagonal honeycombs and related systems. Scr. Mater. 2011, 65, 565–568. [Google Scholar] [CrossRef]
- Ali, M.N.; Busfield, J.J.C.; Rehman, I.U. Auxetic oesophageal stents: Structure and mechanical properties. J. Mater. Sci. Mater. Med. 2014, 25, 527–553. [Google Scholar] [CrossRef] [PubMed]
- Grima, J.N.; Zammit, V.; Gatt, R.; Alderson, A.; Evans, K.E. Auxetic behaviour from rotating semi-rigid units. Phys. Status Solidi B 2007, 244, 866–882. [Google Scholar] [CrossRef]
- Ishibashi, Y.; Iwata, M. A microscopic model of a negative Poisson’s ratio in some crystals. J. Phys. Soc. Jpn. 2000, 69, 2702–2703. [Google Scholar] [CrossRef]
- Grima, J.N.; Gatt, R.; Alderson, A.; Evans, K.E. On the origin of auxetic behaviour in the silicate α-cristobalite. J. Mater. Chem. 2005, 15, 4003. [Google Scholar] [CrossRef]
- Milton, G.W. Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots. J. Mech. Phys. Solids 2013, 61, 1543–1560. [Google Scholar] [CrossRef] [Green Version]
- Milton, G.W. New examples of three-dimensional dilational materials. Phys. Status Solidi B 2015, 252, 1426–1430. [Google Scholar] [CrossRef] [Green Version]
- Prall, D.; Lakes, R.S. Properties of a chiral honeycomb with a poisson’s ratio of −1. Int. J. Mech. Sci. 1997, 39, 305–314. [Google Scholar] [CrossRef]
- Welche, P.R.L.; Heine, V.; Dove, M.T. Negative thermal expansion in beta-quartz. Phys. Chem. Miner. 1998, 26, 63–77. [Google Scholar] [CrossRef]
- Grima, J.N.; Bajada, M.; Scerri, S.; Attard, D.; Dudek, K.K.; Gatt, R. Maximizing negative thermal expansion via rigid unit modes: A geometry-based approach. Proc. R. Soc. A Math. Phys. Eng. Sci. 2015, 471, 20150188. [Google Scholar] [CrossRef] [PubMed]
- Mary, T.A.; Evans, J.S.O.; Vogt, T.; Sleight, A.W. Negative thermal expansion from 0.3 to 1050 Kelvin in ZrW2O8. Science 1996, 272, 90–92. [Google Scholar] [CrossRef] [Green Version]
- Evans, J.S.O.; Mary, T.A.; Sleight, A.W. Negative Thermal Expansion in Sc2(WO4)3. J. Solid State Chem. 1998, 137, 148–160. [Google Scholar] [CrossRef]
- Dove, M.T.; Trachenko, K.O.; Tucker, M.G.; Keen, D.A. Rigid unit modes in framework structures: Theory, experiment and applications. Transform. Process. Miner. 2019, 39, 1–33. [Google Scholar]
- Lim, T.-C. Auxetic Materials and Structures, 1st ed.; Springer: New York, NY, USA, 2015; ISBN 978-981-287-274-6. [Google Scholar]
- Lim, T.C.; Alderson, A.; Alderson, K.L. Experimental studies on the impact properties of auxetic materials. Phys. Status Solidi B 2014, 251, 307–313. [Google Scholar] [CrossRef]
- Bertoldi, K.; Vitelli, V.; Christensen, J.; van Hecke, M. Flexible mechanical metamaterials. Nat. Rev. Mater. 2017, 2, 17066. [Google Scholar] [CrossRef] [Green Version]
- Poźniak, A.A.; Wojciechowski, K.W.; Grima, J.N.; Mizzi, L. Planar auxeticity from elliptic inclusions. Compos. Part B Eng. 2016, 94, 379–388. [Google Scholar] [CrossRef]
- Narojczyk, J.; Wojciechowski, K. Poisson’s Ratio of the f.c.c. Hard Sphere Crystals with Periodically Stacked (001)-Nanolayers of Hard Spheres of Another Diameter. Materials (Basel) 2019, 12, 700. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Narojczyk, J.W.; Kowalik, M.; Wojciechowski, K.W. Influence of nanochannels on Poisson’s ratio of degenerate crystal of hard dimers. Phys. Status Solidi B 2016, 253, 1324–1330. [Google Scholar] [CrossRef]
- Kadic, M.; Tiemo, B.; Schittny, R.; Wegener, M. Metamaterials beyond electromagnetism. Rep. Prog. Phys. 2013, 76, 126501. [Google Scholar] [CrossRef] [PubMed]
- Qu, J.; Kadic, M.; Naber, A.; Wegener, M. Micro-Structured Two-Component 3D Metamaterials with Negative Thermal-Expansion Coefficient from Positive Constituents. Sci. Rep. 2017, 7, 40643. [Google Scholar] [CrossRef]
- Bückmann, T.; Schittny, R.; Thiel, M.; Kadic, M.; Milton, G.W.; Wegener, M. On three-dimensional dilational elastic metamaterials. New J. Phys. 2014, 16, 33032. [Google Scholar] [CrossRef] [Green Version]
- Qu, J.; Kadic, M.; Wegener, M. Poroelastic metamaterials with negative effective static compressibility. Appl. Phys. Lett. 2017, 110, 171901. [Google Scholar] [CrossRef]
- Novak, N.; Vesenjak, M.; Kennedy, G.; Thadhani, N.; Ren, Z. Response of Chiral Auxetic Composite Sandwich Panel to Fragment Simulating Projectile Impact. Phys. Status Solidi B 2019, 1, 1900099. [Google Scholar] [CrossRef]
- Grima, J.N.; Cauchi, R.; Gatt, R.; Attard, D. Honeycomb composites with auxetic out-of-plane characteristics. Comp. Struct. 2013, 106, 150–159. [Google Scholar]
- Strek, T.; Jopek, H.; Wojciechowski, K.W. The influence of large deformations on mechanical properties of sinusoidal ligament structures. Smart Mater. Struct. 2016, 25, 054002. [Google Scholar] [CrossRef]
- Stręk, A.M. Production and study of polyether auxetic foam. Mech. Control 2010, 29, 78–87. [Google Scholar]
- Bertoldi, K.; Reis, P.M.; Willshaw, S.; Mullin, T. Negative Poisson’s Ratio Behavior Induced by an Elastic Instability. Adv. Mater. 2010, 22, 361–366. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Taylor, M.; Francesconi, L.; Gerendás, M.; Shanian, A.; Carson, C.; Bertoldi, K. Low Porosity Metallic Periodic Structures with Negative Poisson’s Ratio. Adv. Mater. 2014, 26, 2365–2370. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Strek, T.; Michalski, J.; Jopek, H. Computational Analysis of the Mechanical Impedance of the Sandwich Beam with Auxetic Metal Foam Core. Phys. Status Solidi B 2019, 256, 1800423. [Google Scholar] [CrossRef]
- Strek, T.; Maruszewski, B.T.; Narojczyk, J.W.; Wojciechowski, K.W. Finite Element Analysis of Auxetic Plate Deformation. J. Non. Cryst. Solids 2008, 354, 4475–4480. [Google Scholar] [CrossRef]
- Brańka, A.C.; Heyes, D.M.; Wojciechowski, K.W. Auxeticity of cubic materials. Phys. Status Solidi B 2009, 246, 2063–2071. [Google Scholar] [CrossRef]
- Branka, A.C.; Heyes, D.M.; Wojciechowski, K.W. Auxeticity of cubic materials under pressure. Phys. Status Solidi B 2011, 248, 96–104. [Google Scholar] [CrossRef]
- Andrade, C.; Ha, C.S.; Lakes, R. Extreme Cosserat elastic cube structure with large magnitude of negative Poisson’s ratio. J. Mech. Mater. Struct. 2018, 13, 93–101. [Google Scholar] [CrossRef]
- Ha, C.S.; Plesha, M.E.; Lakes, R.S. Chiral three-dimensional lattices with tunable Poisson’s ratio. Smart Mater. Struct. 2016, 25, 054005. [Google Scholar] [CrossRef]
- Attard, D.; Grima, J.N. A three-dimensional rotating rigid units network exhibiting negative Poisson’s ratios. Phys. Status Solidi B 2012, 249, 1330–1338. [Google Scholar] [CrossRef]
- Yang, H.; Wang, B.; Ma, L. Mechanical properties of 3D double-U auxetic structures. Int. J. Solids Struct. 2019, 180–181, 13–29. [Google Scholar] [CrossRef]
- Wang, X.T.; Li, X.W.; Ma, L. Interlocking assembled 3D auxetic cellular structures. Mater. Des. 2016, 99, 467–476. [Google Scholar] [CrossRef] [Green Version]
- Lim, T.C. A 3D auxetic material based on intersecting double arrowheads. Phys. Status Solidi B 2016, 253, 1252–1260. [Google Scholar] [CrossRef]
- Larsen, U.D.; Sigmund, O.; Bouwstra, S. Design and fabrication of compliant micromechanisms and structures with negative Poisson’s ratio. J. Microelectromechanical Syst. 1997, 6, 99–106. [Google Scholar] [CrossRef] [Green Version]
- Nye, J.F. Physical Properties of Crystals: Their Representation by Tensors and Matrices; Clarendon Press: Oxford, UK, 1957. [Google Scholar]
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Grima-Cornish, J.N.; Grima, J.N.; Attard, D. A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility. Materials 2020, 13, 79. https://doi.org/10.3390/ma13010079
Grima-Cornish JN, Grima JN, Attard D. A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility. Materials. 2020; 13(1):79. https://doi.org/10.3390/ma13010079
Chicago/Turabian StyleGrima-Cornish, James N., Joseph N. Grima, and Daphne Attard. 2020. "A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility" Materials 13, no. 1: 79. https://doi.org/10.3390/ma13010079
APA StyleGrima-Cornish, J. N., Grima, J. N., & Attard, D. (2020). A Novel Mechanical Metamaterial Exhibiting Auxetic Behavior and Negative Compressibility. Materials, 13(1), 79. https://doi.org/10.3390/ma13010079