Extreme damping in composite materials with negative-stiffness inclusions

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

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

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

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).

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

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).

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

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

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

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

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).

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).

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

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

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).

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).

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).

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).

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

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

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

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

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

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

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

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

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

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

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