Abstract
Detailed new analytical investigations are presented describing the behavior of Class I, II and III viscoelastic Poisson’s ratios (PR). Their previously demonstrated dependence on stress-time histories, which lead to the inability to consider them as universal viscoelastic material properties and the incapacity to produce a general elastic–viscoelastic correspondence principle (EVCP) based, is expanded. A new Class VI PR is analytically derived from the viscoelastic constitutive relations in the Fourier transform (FT) space to achieve the proper FT form of the elastic/viscoelastic correspondence principle, i.e., the elastic-viscoelastic analogy. However, even though this PR Class is a pure universal material property function, it still fails to provide a convenient and useful path to a correspondence principle due to its inopportune constitutive form in real time space vis-à-vis a thermodynamic model with equivalent attributes. Consequently, no general EVCP involving PRs can be formulated. The derived Class VI PRs are equivalent to the defined Class III PRs with 1-D loadings (stresses).
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Poisson, S.-D.: Mémoire sur l’équilibre et le mouvement des corps élastiques. Mém. Acad. Sci. Inst. Fr. 8, 357–570, 623–627 (1829)
Lakes, R.S.: Foam structures with a negative Poisson’s ratio. Science 235, 1038–1040 (1987)
Lakes, R.S.: The time-dependent Poisson’s ratio of viscoelastic materials can increase or decrease. Cell. Compos. 11, 466–469 (1992)
Chen, C.P., Lakes, R.S.: Viscoelastic behaviour of composite materials with conventional—or negative—Poisson’s ratio foam as one phase. J. Mater. Sci. 28, 4288–4299 (1993)
Lakes, R.S.: http://silver.neep.wisc.edu/~lakes/Poisson.html (2005)
Jaglinski, T.M., Lakes, R.S.: Negative stiffness and negative Poisson’s ratio in materials which undergo a phase transformation. In: Wagg, D., Bond, I., Weaver, P., Friswell, M. (eds.) Adaptive Structures—Engineering Applications, pp. 231–246. Wiley, New York (2007)
Shtark, A., Grosbein, H., Sameach, G., Hilton, H.H.: An alternate protocol for determining viscoelastic material properties based on tensile tests without use of Poisson ratios. In: Proceedings of the 2007 International Mechanical Engineering Congress and Exposition. ASME Paper IMECE 2007-41068. Seattle, WA (2007)
Shtark, A., Grosbein, H., Hilton, H.H.: Analytical determination without use of Poisson ratios of temperature dependent viscoelastic material properties based on uniaxial tensile experiments. In: Proceedings of the 2009 International Mechanical Engineering Congress and Exposition. ASME Paper IMECE 2009-10332. Buena Vista, FL (2009)
Shtark, A., Grosbein, H., Sameach, G., Hilton, H.H.: An alternate protocol for determining viscoelastic material properties based on tensile tests without use of Poisson ratios. ASME J. Appl. Mech. JAM08-1361 (2010, accepted)
Christensen, R.M.: Theory of Viscoelasticity—An Introduction, 2nd edn. Academic Press, New York (1982)
Hilton, H.H.: An introduction to viscoelastic analysis. In: Baer, E. (ed.) Engineering, Design for Plastics, pp. 199–276. Reinhold, New York (1964)
Hilton, H.H., Yi, S.: The significance of anisotropic viscoelastic Poisson ratio stress and time dependencies. Int. J. Solids Struct. 35, 3081–3095 (1998)
Hilton, H.H.: Implications and constraints of time independent Poisson ratios in linear isotropic and anisotropic viscoelasticity. J. Elast. 63, 221–251 (2001)
Hilton, H.H.: The elusive and fickle viscoelastic Poisson’s ratio and its relation to the elastic–viscoelastic correspondence principle. J. Mech. Mater. Struct. 4, 1341–1364 (2009)
Arai, M., Kato, Y., Kodera, T.: Characterization of the thermo-viscoelastic property of glass and numerical simulation of the press molding of glass lens. J. Therm. Stresses 32, 1235–1255 (2009)
Manconi, E.: Effect of pre-stress on the global loss factor of viscoelastic laminated curved panels and cylinders. In: Brennan, M. (ed.) Proceedings Tenth International Conference on Recent Advances in Structural Dynamics, Paper, p. 144. University of Southampton, UK (2010)
O’Brien, D.J., Sotos, N.R., White, S.R.: Cure-dependent viscoelastic Poisson’s ratio of epoxy. Exp. Mech. 47, 237–249 (2007)
Lee, H.S., Kim, J.: Determination of viscoelastic Poisson’s ratio and creep compliance from indirect tension test. J. Mater. Civ. Eng. 21, 416–425 (2009)
Beldica, C.E., Hilton, H.H.: Analytical and numerical simulations of experimental determinations of linear viscoelastic constitutive relations. In: Proceedings of the Twelfth International Conference on Composite Materials (ICCM-12), Paris (1999). CD-ROM Volume
Beldica, C.E., Hilton, H.H., Greffe, C.: The relation of experimentally generated wave shapes to viscoelastic material characterizations—analytical and computational simulations. In: Proceedings of the Sixteenth Annual Technical Conference of the American Society for Composites, pp. 1–11, Blacksburg, VA (2001). CD-ROM Vol.
Beldica, C.E., Hilton, H.H.: Analytical and computational simulations of experimental determinations of deterministic and random linear viscoelastic constitutive relations. J. Sandw. Struct. Mater. (2010, accepted)
Freudenthal, A.M.: The Inelastic Behavior of Materials and Structures. Wiley, New York (1950)
Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. Dover, New York (1944)
Hilton, H.H.: On the inadmissibility of separation of variable solutions in linear anisotropic viscoelasticity. Int. J. Mech. Compos. Mater. Struct. 3, 97–100 (1996)
Tschoegl, N.W.: Time dependence in material properties: an overview. Mech. Time-Depend. Mater. 1, 3–31 (1997)
Tschoegl, N.W., Knauss, W.G., Emri, I.: Poisson’s ratio in linear viscoelasticity—a critical review. Mech. Time-Depend. Mater. 6, 3–51 (2002)
Lakes, R.S., Wineman, A.: On Poisson’s ratio in linearly viscoelastic solids. J. Elast. 85, 45–63 (2006)
Khan, K.A., Hilton, H.H.: On inconstant Poisson’s ratios in non-homogeneous elastic media. J. Therm. Stresses 33, 1–8 (2010)
Hilton, H.H.: Viscoelastic Timoshenko beam theory. Mech. Time-Depend. Mater. 13, 1–10 (2009)
Michaeli, M., Shtark, A., Grosbein, H., Hilton, H.H.: A computational protocol for the alternative determination of viscoelastic material properties without Poisson’s ratios. In: Proceedings Times of Polymers and Composites, vol. API 1255, pp. 37–39. American Institute of Physics, College Park (2010)
Ravi-Chandar, K.: Simultaneous measurement of nonlinear bulk and shear relaxation behavior. In: Proceedings of the Second International Conference on Mechanics of Time-Dependent Materials SEM, Ljubljana, Slovenia, pp. 30–31 (1998)
Qvale, Q., Ravi-Chandar, K.: Viscoelastic characterization of polymers under multiaxial compression. Mech. Time-Depend. Mater. 8, 193–214 (2004)
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper is dedicated in memory of my dear friend and cherished colleague Dr. Donald E. Carlson, Professor Emeritus of Theoretical and Applied Mechanics at UIUC, to honor his many fundamental research contributions in mechanics, and for his tireless devotion to his students and to the profession.
Rights and permissions
About this article
Cite this article
Hilton, H.H. Clarifications of Certain Ambiguities and Failings of Poisson’s Ratios in Linear Viscoelasticity. J Elast 104, 303–318 (2011). https://doi.org/10.1007/s10659-010-9296-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10659-010-9296-z
Keywords
- Elastic/viscoelastic correspondence principle
- Integral-differential relations
- Material characterization
- Poisson’s ratio
- Viscoelasticity