Abstract
Poisson's ratio is an elastic constant defined as the ratio of thelateral contraction to the elongation in the infinitesimal uniaxialextension of a homogeneous isotropic body. In a viscoelastic materialPoisson's ratio is a function of time (or frequency) that depends on thetime regime chosen to elicit it. It is important as one of the materialfunctions that characterize bulk behavior.
This paper develops the linear theory of the time- orfrequency-dependent Poisson's ratio, and it reviews work on itsexperimental determination. The latter poses severe difficulties in viewof the high accuracy required. Thus, reliable information on theviscoelastic Poisson's ratio is as yet rather scanty.
The paper also reports on attempts to measure the Poisson's ratioof a viscoelastic material as a function of temperature. Lateralcontraction in creep and at constant rate of extension receivesattention as well.
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References
Adams, R.D. and Peppiatt, N.A., 'Effect of Poisson's ratio strains in adherends on stresses of an idealized lap joint', J. Strain Anal. 8, 1973, 134-139.
Bauer C.L. and Farris, R.J., 'Determination of Poisson's ratio for polyimide films', Polym. Engrg. Sci. 29, 1989, 1107-1110.
Baumgaertel, M. and Winter, H.H., 'Interrelation between continuous and discrete relaxation time spectra', J. Non-Newtonian Fluid Mech. 44, 1992, 15-36.
Blatz, P.J. and Ko,W.L., 'Application of finite elastic theory to the deformation of rubbery materials', Trans. Soc. Rheol. 6, 1962, 223-251.
Chang, W.V., Bloch, R. and Tschoegl, N.W., 'Study of the viscoelastic behavior of uncrosslinked (gum) rubbers in moderately large deformations', J. Polymer Sci., Polymer Phys. Ed. 15, 1977, 923-944.
Clayton, D., Darlington, M.W. and Hall, M.M., 'Tensile creep modulus, creep lateral contraction ratio and torsional creep measurements on small nonrigid specimens', J. Phys. E: Sci. Instr. 6, 1973, 218-226.
Crowson, R.J. and Arridge, R.G.C., 'Linear viscoelastic properties of epoxy resin polymers in dilatation and shear in the glass transition region. 1. Time-temperature Superposition of creep data', Polymer 20, 1979a, 737-746.
Crowson, R.J. and Arridge, R.G.C., 'Linear viscoelastic properties of epoxy resin polymers in dilatation and shear in the glass transition region: 2. Measurement of the glass transition temperature', Polymer 20, 1979b, 747-754.
Darlington, M.W. and Saunders, D.W., 'The tensile creep behaviour of cold-drawn low-density polyethylene', J. Phys. D: Appl. Phys. 3, 1970, 535-549.
Delin, M., Rychwalski, R.W., Kubát, M.J. and Kubát, J., 'Volume changes during stress relaxation in polyethylene', Rheol. Acta 34, 1995, 182-195.
Deng, T.H. and Knauss, W.G., 'The temperature and frequency dependence of the bulk compliance of poly(vinyl acetate). A re-examination', Mech. Time-Dependent Mater. 1, 1997, 33-49.
Emri, I. and Tschoegl, N.W., 'Generating line spectra from experimental responses. Part I: Relaxation modulus and creep compliance', Rheol. Acta 32, 1993, 311-321.
Emri, I. and Tschoegl, N.W., 'Generating line spectra from experimental responses. Part IV: Application to experimental data', Rheol. Acta 33, 1994, 60-70.
Emri, I. and Tschoegl, N.W., 'An iterative computer algorithm for generating line spectra from linear viscoelastic response functions', Internat. J. Polym. Mater. 40, 1998, 55-79.
Emri, I., Nikonov, A. and Tschoegl, N.W., 'Numerical errors in the interconversion of creep and relaxation functions', Rheol. Acta, 2002, to be submitted.
Eringen, A.C., Non-Linear Theory of Continuous Media, McGraw-Hill, New York, 1962, 177.
Fedors, R.F. and Hong, S.D., 'A new technique for measuring Poisson's ratio', J. Polym. Sci., Polym. Phys. Ed. 20, 1982, 777-781.
Fellahi, B., Fisa, B. and Favis, B.D., 'Welding strength in injection molded HDPE/PA6 blends. Influence of interfacial modification', J. Appl. Polym. Sci. 57, 1995, 1319-1332.
Ferry, J.D., Viscoelastic Properties of Polymers, 3rd edn, John Wiley and Sons, New York, 1980.
Fisa, B., Favis, B.D. and Bourgeois, S., 'Injection molding of polypropylene/polycarbonate blends', Polym. Engrg. Sci. 30, 1990, 1051.
Freudenthal, A.M. and Henry, L.A., 'On Poisson's ratio in linear viscoelastic propellants', Progr. Aeronautics Rocketry 1, 1960, 33-66. 34-66.
Gent, A.N. and Hwang, Y.-C., 'Elastic behavior of a double layer bonded between two rigid spheres', Rubber Chem. Tech. 61, 1988, 630-638.
Gilmour, I.W., Trainor, A. and Haward, R.N., 'Elastic moduli of glassy polymers at low strains', J. Appl. Polym. Sci. 23, 1979, 3129-3138.
Giovagnoni, M., 'On the direct measurement of the dynamic Poisson's ratio', Mech. Mater. 17, 1994, 33-46.
Harris, J.A. and Adams, R.D., 'Strength predictions of bonded single loop joints by non-linear FEM', Internat. J. Adhesion Adhesives 4, 1984, 65-78.
Häusler K.G., Hauptmann, P., Meischner, C., Fedtke, M., Hartel, E. and Wartewig, S., 'Ultrasonic investigations of modified epoxies', Polym. Commun. 28, 1987, 154-157.
Heydemann, P., 'On the minimum of Poisson's ratio in polymers', Kolloid-Z. u. Z. f. Polymere 193, 1963, 12-15.
Hopkins, I.L. and Hamming, R.W., 'On creep and relaxation', J. Appl. Phys. 28, 1957, 906.
Karger-Kocsis, J. and Csikai, I., 'Skin-core morphology and failure of injection-molded specimens of impact-modified polypropylene blends', Polym. Engrg. Sci. 27, 1987, 241.
Kästner, S. and Pohl, G., 'Ein Beitrag zur Frage der vollständigen Erfassung des mechanischen Relaxationsverhaltens der Polymeren', Kolloid-Z. u. Z. f. Polymere 191, 1963, 114.
Kimoto M., Nagata, I., Minowa, A., Moriwaki, K. and Watanabe, T., 'Evaluation of disbondings and measurement of Poisson's ratio for plastic composites using holographic interferometry', J. Appl. Polym. Sci. 40, 1990, 1085-1093.
Kinloch, A.J., Adhesion and Adhesives, Chapman and Hall, London, 1990.
Knauss, W.G., 'The investigation of the mechanical properties of thermoviscoelastic materials', Soc. Exp. Mech. 1, 1992, 22-26 (Proceedings of the VII International Congress on Experimental Mechanics, Las Vegas, NV).
Knauss,W.G. and Emri, I., 'Non-linear viscoelasticity based on free volume consideration', Comput, & Structures 13, 1981, 123-128; also in: Computational Methods in Nonlinear Structure and Solid Mechanics, A.K. Noor and H.G. McComb (eds), Pergamon Press, Oxford, 1981, 123-128.
Kono, R., 'The dynamic bulk viscosity of polystyrene and polymethyl methacrylate', J. Phys. Soc. Japan 15(4), 1960, 718-725.
Kono, R., 'The dynamic bulk and shear viscosity of high polymers. I', J. Phys. Soc. Japan 16, 1961a, 1580-1586.
Kono, R., 'The dynamic bulk and shear viscosities of polyvinylchloride', J. Phys. Soc. Japan 16, 1961b, 1793-1794.
Kono, R. and Yoshizaki, H., 'Viscoelastic properties of polyvinyl-i-butyl ethers at high frequencies', Japan J. Appl. Phys. 12(3), 1973, 445-457.
Koppelmann, V.J., 'Ñber den dynamischen Elastizitätsmodul von Polymethacrylsäuremethylester bei sehr tiefen Frequenzen', Kolloid-Z. 164, 1959, 31-34.
Kubát, M.J., Vernel, J., Rychwalski, R.W. and Kubát, J., 'Bulk moduli from physical aging and stress relaxation data', Polym. Engrg. Sci. 38(8), 1998, 1261.
Kugler, H.P., Stacer, R.G. and Steimle, C., 'Direct measurements of Poisson's ratio in elastomers', Rubber Chem. Tech. 63, 1990, 473-487.
Ladizesky, N.H. and Ward, I.M., 'Determination of Poisson's ratio and Young's modulus of lowdensity polyethylene', J. Macromol. Sci.-Phys. B5(4), 1971, 661-692.
Laufer, Z., Diamant, Y., Gill, M. and Fortuna, G., 'A simple dilatometric method for determining Poisson's ratio of nearly incompressible elastomers', Internat. J. Polym.Mater. 6, 1978, 159-174.
Lee, E.H., 'Viscoelastic stress analysis', in Structural Mechanics, J.N. Goodier and N.J. Hoff (eds), Pergamon Press, Oxford, 1960, 456-482.
Lobdell, A.J., Shinopulos, G.F. and Fillio, D.N., 'An instrument to measure transverse strain', Mater. Res. Stand. 4, 1964, 8-11.
Lu, H., Zhang, X. and Knauss, W.G., 'Uniaxial, shear and Poisson relaxation and their conversion to bulk relaxation', Polymer Composites 18(2), 1997, 211-222; J. Polym. Sci. Engrg. 37(6), 1997, 1053-106.
Malvern, L.E., Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, NJ, 1969, 293.
Michaeli, W. and Dassow, J., 'Describing Poisson's ratio of thermoplastics as a non-linear viscoelastic parameter', in Proceedings 52nd Annual Technical Conference, ANTEC '94, San Francisco, CA, Society of Plastic Engineers, Brookfield, 1994, 1804-1806. Reprinted in British Plastics and Rubber, MCM Publishing, London, 1995, 21-24.
Migwi, C.M., Darby, M.I., Wolstenholm, G.H., Yates, B., Duffy, R. and Moss, M., 'A method for determining the shear modulus and Poisson's ratio of polymer materials', J. Mater. Sci. 29, 1994, 3430-3432.
Morita, E., Kono, R. and Yoshizaki, H., 'Bulk and shear relaxation processes in poly-i-butyl methacrylate', Japan J. Appl. Phys. 7(5), 1968, 451-461.
Nikonov, A., Tschoegl, N.W. and Emri, I., 'Numerical errors in the interconversion of creep and relaxation functions', Rheol. Acta, 2001, submitted.
Onogi, S. and Ui, K., 'Frequency and temperature dispersions of high polymers', J. Colloid Sci. 11, 1956, 214.
Philippoff, W. and Brodnyan, J., 'Preliminary results in measuring dynamic compressibilities', J. Appl. Phys. 26(7), 1955, 846-849.
Richardson, I.D. and Ward, I.M., 'Temperature dependence of the Poisson's ratios in low-density polyethylene with parallel lamellas morphology', J. Polym. Sci. Polym. Phys. Ed. 16, 1978, 667-678.
Rigby, Z., 'Phase shifts in stress-strain relationships of viscoelastic materials', Rheol. Acta 5, 1965, 28-29.
Rigbi, Z., 'The value of Poisson's ratio of viscoelastic materials', Appl. Polym. Symp. 5, 1967, 1-8.
Samarin, M., Tschoegl, N.W. and Emri, I., 'The simultaneous determination of Young's modulus and the viscoelastic Poisson's ratio', Mech. Time-Dependent Mater., 2002, to be submitted.
Sane, S. and Knauss,W.G., 'The time-dependent bulk response of poly(methyl methacrylate)', Mech. Time-Dependent Mater. 5, 2001, 293-324.
Smith, T.L., 'Volume changes and dewetting in glass bead-Polyvinyl chloride elastomeric composites under large deformations', Trans. Soc. Rheol. 3, 1959, 113-136.
Summerscales, J. and Fry, S.A., 'Poisson's ratio in fibre-reinforced polymer composites with a high void content', J. Mater. Sci. Lett. 13, 1994, 912-914.
Theocaris, P.S., 'Creep and relaxation contraction ratio of linear viscoelastic materials', J. Mech. Phys. Solids 12, 1964, 125-138.
Thomson, K.C., 'On the complex Poisson's ratio of a urethane rubber compound', J. Appl. Polym. Sci. 10, 1966, 1133-1136.
Tschoegl, N.W., The Phenomenological Theory of Linear Viscoelastic Behavior, Springer-Verlag, Heidelberg, 1989.
Tschoegl, N.W., 'Time dependence in material properties: An overview', Mech. Time-Dependent Mater. 1, 1997, 1-31.
Tschoegl, N.W. and Emri, I., 'Generating line spectra from experimental responses. Part III: Interconversion between relaxation and retardation behavior', Internat. J. Polym. Mater. 18, 1992, 117-127.
Tschoegl, N.W. and Emri, I., 'Generating line spectra from experimental responses. Part II: Storage and loss functions', Rheol. Acta 32, 1993, 322-327.
Tschoegl, N.W., Knauss, W.G. and Emri, I., 'The effect of temperature and pressure on the mechanical properties of thermo-and/or piezorheologically simple polymeric materials in thermodynamic equilibrium-A critical review', Mech. Time-Dependent Mater. 6, 2002, 53-99.
Tsou, A.H., Greener, J. and Smith, G.D., 'Stress relaxation of polymer films in bending', Polymer 36(5), 1995, 949-954.
van der Varst, P.G.Th. and Kortsmit,W.G., 'Notes on the lateral contraction of linear isotropic viscoelastic materials', Appl. Mech. 62, 1992, 338-346.
Waterman, H.A., 'Determination of the complex moduli of viscoelastic materials with the ultrasonic pulse method (Part I)', Kolloid-Z. u. Z. f. Polymere 192, 1963a, 1-8.
Waterman, H.A., 'Determination of the complex moduli of viscoelastic materials with the ultrasonic pulse method (Part II)', Kolloid-Z. u. Z. f. Polymere 192, 1963b, 9-16.
Waterman, H.A., 'Relation between loss angles in isotropic linear viscoelastic materials', Rheol. Acta 16, 1977, 31-42.
Weber, H., Wolf, T. and Dünger, U., 'Determination of relaxation moduli and Poisson's ratio in uniaxially loaded solid polyethylene foam specimens as part of full material characterization', Mech. Time-Dependent Mater. 1, 1997, 195-208.
Wilson, I., Cunningham, A. and Ward, I.M., 'The determination of Poisson's ratio compliances for polyethylene terephthalate sheets using a Michelson interferometer', J. Mater Sci. 11, 1976, 2181-2188.
Wilson, I., Ladizesky, N.H. and Ward, I.M., 'The determination of Poisson ratio and extensional modulus for polyethylene terephthalate sheets by an optical technique', J. Mater. Sci. 11, 1976, 2177-2180.
Yee, A.F., 'Dynamic-mechanical studies of some polymers containing the bisphenol-A units', ACS Polymer Preprints 21(2), 1980, 285-286.
Yee, A.F. and Takemori, M.T., 'A new technique for measuring volume and shear relaxation in solid polymers: Dynamic Poisson's ratio', ACS Polymer Preprints 20(1), 1979, 758-761.
Yee, A.F. and Takemori, M.T., 'Dynamic bulk and shear relaxation in glassy polymers. I. Experimental techniques and results on PMMA', J. Polym. Sci., Polym. Phys. Ed. 20, 1982, 205-224.
Zihlif, A.M., Duckett, R.A. and Ward, I.M., 'The determination of the lateral compliances and Poisson's ratios for highly oriented polyethylene sheets', J. Mater. Sci. 17, 1982, 1125-1130.
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Tschoegl, N., Knauss, W.G. & Emri, I. Poisson's Ratio in Linear Viscoelasticity – A Critical Review. Mechanics of Time-Dependent Materials 6, 3–51 (2002). https://doi.org/10.1023/A:1014411503170
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DOI: https://doi.org/10.1023/A:1014411503170