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Mechanical metamaterials with negative compressibility transitions

Nature Materials volume 11, pages 608–613 (2012)Cite this article

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Abstract

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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Figure 1: Negative compressibility contrasted with other effects.
Figure 2: Constituents, metamaterial, and resulting hysteresis loops.
Figure 3: Effective energy barrier and the temperature dependence of the transitions.
Figure 4: Physical examples of stress-induced negative compressibility and strain-induced force amplification transitions.

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Acknowledgements

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.).

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Authors and Affiliations

  1. Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA

    Zachary G. Nicolaou & Adilson E. Motter

  2. Northwestern Institute on Complex Systems, Northwestern University, Evanston, Illinois 60208, USA

    Adilson E. Motter

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  1. Zachary G. Nicolaou
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  2. Adilson E. Motter
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Contributions

Z.G.N. and A.E.M. designed the research. Z.G.N. performed the numerical and analytical calculations. A.E.M. supervised the research and the analysis of the results. Both authors contributed to the preparation of the manuscript.

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Correspondence to Adilson E. Motter.

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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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