When tensioned, ordinary materials expand along the direction of the applied force. Here, we explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). Continuous contraction of a material in the same direction of an applied tension, and in response to this tension, is inherently unstable. The conceptually similar effect we demonstrate can be achieved, however, through destabilizations of (meta)stable equilibria of the constituents. These destabilizations give rise to a stress-induced solid–solid phase transition associated with a twisted hysteresis curve for the stress–strain relationship. The strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. We suggest that the proposed materials could be useful for the design of actuators, force amplifiers, micromechanical controls, and protective devices.
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Veselago, V. G. The electrodynamics of substances with simultaneously negative values of ɛ and μ. Sov. Phys. Usp. 10, 509–514 (1968) Original Publication in Russian, 1967.
Smith, D. R., Padilla, W. J., Vier, D. C., Nemat-Nasser, S. C. & Schultz, S. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000).
Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292, 77–79 (2001).
Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000).
Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006).
Zhang, S., Yin, L. & Fang, N. Focusing ultrasound with an acoustic metamaterial network. Phys. Rev. Lett. 102, 194301 (2009).
Baughman, R. H., Stafström, S., Cui, C. & Dantas, S. O. Materials with negative compressibilities in one or more dimensions. Science 279, 1522–1524 (1998).
Lee, Y., Vogt, T., Hriljac, J. A., Parise, J. B. & Artioli, G. Pressure-induced volume expansion of zeolites in the natrolite family. J. Am. Chem. Soc. 124, 5466–5475 (2002).
Vakarin, E. V., Duda, Y. & Badiali, J. P. Negative linear compressibility in confined dilatating systems. J. Chem. Phys. 124, 144515 (2006).
Grima, J. N., Attard, D. & Gatt, R. Truss-type systems exhibiting negative compressibility. Phys. Status Solidi B 245, 2405–2414 (2008).
Gatt, R. & Grima, J. N. Negative compressibility. Phys. Status Solidi RRL 2, 236–238 (2008).
Liu, Z. et al. Locally resonant sonic materials. Science 289, 1734–1736 (2000).
Fang, N. et al. Ultrasonic metamaterials with negative modulus. Nature Mater. 5, 452–456 (2006).
Sheng, P., Xiao, R-F., Wen, W-J. & Zheng, Y. L. Composite materials with negative elastic constants. US patent 6,576,333 (2003).
Lakes, R. S., Lee, T., Bersie, A. & Wang, Y. C. Extreme damping in composite materials with negative-stiffness inclusions. Nature 410, 565–567 (2001).
Jaglinski, T., Kochmann, D., Stone, D. & Lakes, R. S. Composite materials with viscoelastic stiffness greater than diamond. Science 315, 620–622 (2007).
Reichl, L. E. A Modern Course in Statistical Physics (Wiley, 2009).
Lakes, R. S. Foam structures with a negative Poisson’s ratio. Science 235, 1038–1040 (1987).
Baughman, R. H., Shacklette, J. M., Zakhidov, A. A. & Stafström, S. Negative Poisson’s ratio as a common feature of cubic metals. Nature 392, 362–365 (1998).
Janmey, P. A., McCormick, M. E., Rammensee, S., Leight, J. L., Georges, P. C. & MacKintosh, F. C. Negative normal stress in semiflexible biopolymer gels. Nature Mater. 6, 48–51 (2007).
Moore, B., Jaglinski, T., Stone, D. S. & Lakes, R. S. Negative incremental bulk modulus in foams. Phil. Mag. Lett. 86, 651–659 (2006).
Goodwin, A. L., Keen, D. A. & Tucker, M. G. Large negative linear compressibility of Ag3[Co(CN)6]. Proc. Natl Acad. Sci. USA 105, 18708–18713 (2008).
Fortes, D. A., Suard, E. & Knight, K. S. Negative linear compressibility and massive anisotropic thermal expansion in methanol monohydrate. Science 331, 742–746 (2011).
Braess, D., Nagurney, A. & Wakolbinger, T. On a paradox of traffic planning. Transp. Sci. 39, 446–450 (2005) Original Publication in German, 1968.
Roughgarden, T. Selfish Routing and the Price of Anarchy (MIT Press, 2005).
Beckmann, M. J., McGuire, C. B. & Winsten, C. B. Studies in the Economics of Transportation (Yale Univ. Press, 1956).
Pigou, A. C. The Economics of Welfare (Macmillan, 1920).
Cohen, J. E. & Horowitz, P. Paradoxical behaviour of mechanical and electrical networks. Nature 352, 699–701 (1991).
Mishima, O. & Stanley, H. E. The relationship between liquid, supercooled and glassy water. Nature 396, 329–335 (1998).
Otsuka, K. & Wayman, C. M. Shape Memory Materials (Cambridge Univ. Press, 1998).
Abeyaratne, R. & Knowles, J. K. Evolution of Phase Transitions: A Continuum Theory (Cambridge Univ. Press, 2006).
Puglisi, G. & Truskinovsky, L. Mechanics of a discrete chain with bi-stable elements. J. Mech. Phys. Solids 48, 1–27 (2000).
Mallikarachchi, H. M. Y. C. & Pellegrino, S. Quasi-static folding and deployment of ultrathin composite tape-spring hinges. J. Spacecr. Rockets 48, 187–198 (2011).
Andersen, H. C. Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72, 2384–2393 (1980).
Martyna, G. J., Klein, M. L. & Tuckerman, M. Nosé–Hoover chains: The canonical ensemble via continuous dynamics. J. Chem. Phys. 97, 2635–2643 (1992).
This study was supported by the Materials Research Science and Engineering Center at Northwestern University through Grant No. DMR-0520513 (Z.G.N.), the National Science Foundation Grants No. DMS-0709212 (Z.G.N. and A.E.M.) and No. DMS-1057128 (A.E.M.), a National Science Foundation Graduate Research Fellowship (Z.G.N.) and a Sloan Research Fellowship (A.E.M.).
The authors declare no competing financial interests.
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Nicolaou, Z., Motter, A. Mechanical metamaterials with negative compressibility transitions. Nature Mater 11, 608–613 (2012). https://doi.org/10.1038/nmat3331
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