Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Extreme damping in composite materials with negative-stiffness inclusions

Nature volume 410, pages 565–567 (2001)Cite this article

Abstract

When a force deforms an elastic object, practical experience suggests that the resulting displacement will be in the same direction as the force. This property is known as positive stiffness1. Less familiar is the concept of negative stiffness, where the deforming force and the resulting displacement are in opposite directions. (Negative stiffness is distinct from negative Poisson's ratio2,3,4,5,6, which refers to the occurrence of lateral expansion upon stretching an object.) Negative stiffness can occur, for example, when the deforming object has stored7 (or is supplied8 with) energy. This property is usually unstable, but it has been shown theoretically9 that inclusions of negative stiffness can be stabilized within a positive-stiffness matrix. Here we describe the experimental realization of this composite approach by embedding negative-stiffness inclusions of ferroelastic vanadium dioxide in a pure tin matrix. The resulting composites exhibit extreme mechanical damping and large anomalies in stiffness, as a consequence of the high local strains that result from the inclusions deforming more than the composite as a whole. Moreover, for certain temperature ranges, the negative-stiffness inclusions are more effective than diamond inclusions for increasing the overall composite stiffness. We expect that such composites could be useful as high damping materials, as stiff structural elements or for actuator-type applications.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Experimental torsional compliance (inverse stiffness) and mechanical damping, tanδ, versus temperature.
Figure 2: Theoretical shear modulus G′ (real part) and mechanical damping, tanδ, versus inclusion shear modulus Ginc normalized to matrix shear modulus G′m, of Hashin–Shtrikman composite containing 1% of spherical particulate inclusions by volume.

Similar content being viewed by others

References

  1. Timoshenko, S. P. & Goodier, J. N. Theory of Elasticity 3rd edn (McGraw-Hill, New York, 1970).

    MATH  Google Scholar 

  2. Lakes, R. S. Foam structures with a negative Poisson's ratio. Science 235, 1038–1040 (1987).

    Article  ADS  CAS  Google Scholar 

  3. Lakes, R. S. Advances in negative Poisson's ratio materials. Adv. Mater. 5, 293–296 (1993).

    Article  CAS  Google Scholar 

  4. Haeri, A. Y., Weidner, D. J. & Parise, J. B. Elasticity of α-cristobalite: a silicon dioxide with a negative Poisson's ratio. Science 257, 650–652 (1992).

    Article  ADS  Google Scholar 

  5. Rothenburg, L., Berlin, A. A. & Bathurst, R. J. Microstructure of isotropic materials with negative Poisson's ratio. Nature 354, 470–472 (1991).

    Article  ADS  Google Scholar 

  6. Baughman, R. H., Shacklette, J. M., Zakhidov, A. A. & Stafstrom, S. Negative Poisson's ratios as a common feature of cubic metals. Nature 392, 362–365 (1998).

    Article  ADS  CAS  Google Scholar 

  7. Thompson, J. M. T. Stability prediction through a succession of folds. Phil. Trans. R. Soc. Lond. 292, 1–23 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  8. Thompson, J. M. T. ‘Paradoxical’ mechanics under fluid flow. Nature 296, 135–137 (1982).

    Article  ADS  Google Scholar 

  9. Lakes, R. S. & Drugan, W. J. Stiff elastic composite materials with a negative stiffness phase. J. Mech. Phys. Solids (submitted).

  10. Heckingbottom, R. & Linnett, J. W. Structure of vanadium dioxide. Nature 194, 678 (1962).

    Article  ADS  CAS  Google Scholar 

  11. Paquet, D. & Leroux-Hagon, P. Electron correlations and electron-lattice interactions in the metal-insulator ferroelastic transition in VO2: a thermodynamical study. Phys. Rev. B 22, 5284–5301 (1979).

    Article  ADS  Google Scholar 

  12. Zhang, J. X., Yang, Z. H. & Fung, P. C. W. Dissipation function of the first-order phase transformation in VO2 ceramics by internal friction measurements. Phys. Rev. B 52, 278–284 (1995).

    Article  ADS  CAS  Google Scholar 

  13. Handbook of Chemistry and Physics C-40 12–40 (CRC Press, Boca Raton, Florida, 1996).

  14. Brodt, M., Cook, L. S. & Lakes, R. S. Apparatus for measuring viscoelastic properties over ten decades: refinements. Rev. Sci. Instrum. 66, 5292–5297 (1995).

    Article  ADS  CAS  Google Scholar 

  15. Lakes, R. S. & Quackenbush, J. Viscoelastic behaviour in indium tin alloys over a wide range of frequency and time. Phil. Mag. Lett. 74, 227–232 (1996).

    Article  ADS  CAS  Google Scholar 

  16. Bramble, J. H. & Payne, L. E. On the uniqueness problem in the second boundary value problem in elasticity. Proc. 4th Natl Cong. Appl. Mech. 469–473 (American Society of Mechanical Engineers, Berkeley, California, 1963).

  17. Knowles, J. K. & Sternberg, E. On the failure of ellipticity and the emergence of discontinuous gradients in plane finite elastostatics. J. Elasticity 8, 329–379 (1978).

    Article  MathSciNet  Google Scholar 

  18. Hashin, Z. & Shtrikman, S. A variational approach to the theory of the elastic behavior of multiphase materials. J. Mech. Phys. Solids 11, 127–140 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  19. Read, W. T. Stress analysis for compressible viscoelastic materials. J. Appl. Phys. 21, 671–674 (1950).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. Hashin, Z. Viscoelastic behavior of heterogeneous media. J. Appl. Mech. Trans. ASME 32E, 630–636 (1965).

    Article  ADS  Google Scholar 

  21. Lakes, R. S. Extreme damping in composite materials with a negative stiffness phase. Phys. Rev. Lett. (in the press).

  22. Rosakis, P., Ruina, A. & Lakes, R. S. Microbuckling instability in elastomeric cellular solids. J. Mater. Sci. 28, 4667–4672 (1993).

    Article  ADS  Google Scholar 

  23. Salje, E. Phase Transitions in Ferroelastic and Co-elastic Crystals 10, 72 (Cambridge Univ. Press, Cambridge, 1990).

    Google Scholar 

  24. Lakes, R. S. Extreme damping in compliant composites with a negative stiffness phase. Phil. Mag. Lett. 81, 95–100 (2001).

    Article  ADS  CAS  Google Scholar 

  25. Ren, X. & Otsuka, K. Origin of rubber-like behaviour in metal alloys. Nature 389, 579–583 (1997).

    Article  ADS  CAS  Google Scholar 

  26. Cremer, L., Heckl, M. A. & Ungar, E. E. Structure Borne Sound 2nd edn 243–247 (Springer, Berlin, 1988).

    Book  Google Scholar 

  27. Pugh, J. W., Rose, R. M., Paul, I. L. & Radin, E. L. Mechanical resonance spectra in human cancellous bone. Science 181, 271–272 (1973).

    Article  ADS  Google Scholar 

  28. Falk, F. Model free energy, mechanics, and thermodynamics of shape memory alloys. Acta Metall. 28, 1773–1780 (1980).

    Article  CAS  Google Scholar 

  29. Duffy, W. Acoustic quality factor of aluminum alloys from 50 mK to 300 K. J. Appl. Phys. 68, 5601–5609 (1990).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank W. Drugan and R. Cooper for supportive comments and discussions. This work was supported by the NSF.

Author information

Authors and Affiliations

  1. Department of Engineering Physics,

    R. S. Lakes, A. Bersie & Y. C. Wang

  2. Engineering Mechanics Program,

    R. S. Lakes, A. Bersie & Y. C. Wang

  3. Biomedical Engineering Department,

    R. S. Lakes & T. Lee

  4. Materials Science Program,

    R. S. Lakes

  5. Rheology Research Center, University of Wisconsin-Madison, 147 Engineering Research Building, 1500 Engineering Drive, Madison, 53706-1687, Wisconsin, USA

    R. S. Lakes

Authors
  1. R. S. Lakes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Bersie
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Y. C. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. S. Lakes.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lakes, R., Lee, T., Bersie, A. et al. Extreme damping in composite materials with negative-stiffness inclusions. Nature 410, 565–567 (2001). https://doi.org/10.1038/35069035

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/35069035

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing