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Characterization of Polyurethane Rubber at High Deformation Rates

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Polyurethane rubber materials have widespread usage in large-deformation energy absorption and dissipation applications. Accurate design modeling with these materials requires an appropriate constitutive material model that accounts for both static (low strain rate) and dynamic (high strain rate) responses. A common modeling approach is the use of hyper-viscoelastic formulations, which couple quasi-static hyperelastic with dynamic viscoelastic responses and describe the material response over a range of deformation rates. In this work the effectiveness of two models, the Modified Quasi-Linear Viscoelastic and Non-Linear Hyper-Viscoelastic, are investigated to describe the high-rate behaviour of two different grades of polyurethane rubber. From quasi-static, uniaxial compression tests, a Rivlin hyperelastic formulation was found to describe the low-rate response well. High-rate, uniaxial compressions test were performed using a Polymeric Split Hopkinson Pressure Bar (PSHPB), supported by high-speed photography. In general, it was found that the Modified Quasi-Linear Viscoelastic model did not fit the experimental data well due to its limited non-linear terms, while the Non-Linear Hyper-Viscoelastic provided very good agreement.

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  1. 1.

    General Motors Limited, 2004, Dummy Timeline, http://www.gm.com/company/gmability/safety/protect_occupants/dummies/dummy_timeline_010702.html.

  2. 2.

    Bourget D, Anctil B, Doman DA, Cronin DS (2002) Development of a surrogate thorax for BABT studies. In: Proceedings from Personal Armour Systems Symposium 2002, The Netherlands.

  3. 3.

    Sharma A, Shukla A (2002) Mechanical characterization of soft materials using high speed photography and split Hopkinson pressure bar technique. J Mater Sci 37:1005–1017.

  4. 4.

    Vuoristo T, Kuokkala VT (2002) Creep, recovery and high strain rate response of soft roll cover materials. Mech Mater 34:493–504.

  5. 5.

    Yang LM, Shim VPW, Lim CT (2000) A Visco-hyperelastic approach to modeling the constitutive behaviour of rubber. Int J Impact Eng 24:545–560.

  6. 6.

    Fung YC (1972) Stress–strain history relations of soft tissues in simple elongation. In: Fung YC, Perrone N, Anliker M (eds) Biomechanics: its foundations and objectives, Prentice-Hall, United States of America.

  7. 7.

    Feng WW (1985) On finite deformation of viscoelastic rotating disks. Int J Non-Linear Mech 20:21–26.

  8. 8.

    Feng WW (1992) A recurrence formula for viscoelastic constitutive equations. Int J Non-Linear Mech 27:675–678.

  9. 9.

    Hallquist JO (1998) LS-DYNA theory manual. Livermore Software Technology Corporation, United States of America.

  10. 10.

    Best TM, McElhaney J, Garrett WE, Meyers BS (1994) Characterization of the passive responses of live skeletal muscle using the quasi-linear theory of viscoelasticity. J Biomech 27:413–419.

  11. 11.

    Sarver JJ, Robinson PS, Elliot DM (2003) Methods for quasi-linear viscoelastic modeling of soft tissue: Application to incremental stress-relaxation. J Biomech Eng 125:754–758.

  12. 12.

    Doman D (2004) Modeling of the high rate behaviour ofpolyurethane rubber, MASc thesis, University of Waterloo.

  13. 13.

    Van Sligtenhorst C, Cronin D, Brodland GW (2005) High strain rate compressive properties of bovine muscle tissue found using a split hopkinson bar apparatus. In Press., J Biomech.

  14. 14.

    Salisbury CP (2001) Spectral analysis of wave propagation through a polymeric Hopkinson Bar, MASc thesis, University of Waterloo, Canada.

  15. 15.

    Smooth-On Inc., http://www.smooth-on.com/liqrubr.htm.

  16. 16.

    Rivlin RS (1960) Some topics in finite elasticity. Proceedings of the First Symposium on Naval Structural Mechanics, pp. 169–198.

  17. 17.

    Puso MA, Weiss JA (1998) Finite element implementation of anisotropic quasi-linear visocelasticity using a discrete spectrum approximation. J Biomech Eng 120:62–70.

  18. 18.

    Mooney M (1940) A theory of large elastic deformation. J Appl Phys 11:582–592.

  19. 19.

    Brown RP (1996) Physical testing of rubber, 3rd edn. Chapman and Hall, United Kingdom.

  20. 20.

    Hibbitt, Karlsson, and Sorenson Inc. (1997) ABAQUS Theory manual version 5.7, United States of America.

  21. 21.

    Lockett FJ (1972) Nonlinear viscoelastic solids. Academic Press Ltd., United Kingdom.

  22. 22.

    Truesdell C, Noll W (1965) The non-linear field theories of mechanics. Springer-Verlag, Germany.

  23. 23.

    Gray GT, Blumethal WR (2000) Split-Hopkinson pressure bar testing of soft materials. In: ASM Handbook. Volume 8: Mechanical testing and evaluation, 2nd edn. American Society for Metals, United States of America.

  24. 24.

    Brands DWA, Peters GWM, Bovendeerd PHM (2004) Design and numerical implementation of a 3-D non-linear viscoelastic constitutive model for brain tissue during impact. J Biomech 37:127–134.

  25. 25.

    Clamroth R (1981) Determination of viscoelastic properties by dynamic testing. Polym Test 2:263–286.

  26. 26.

    Kolsky H (1949) An investigation of the mechanical properties of materials at high rates of loading. Proc Phys Soc B 62:676–700.

  27. 27.

    Bacon C (1998) An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson Bar. Exp Mech 38:242–249.

  28. 28.

    Davies EDM, Hunter SC (1963) The dynamic compression testing of solids by the method of the split Hopkinson pressure bar. J Mech Phys Solids 11:155–179.

  29. 29.

    Dioh NN, Leevers PS, Williams JG (1993) Thickness effects in split Hopkinson pressure bar tests. Polymer 34:4230–4234.

  30. 30.

    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C: The art of scientific computing, 2nd edn. Cambridge University Press, United States of America.

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Correspondence to D. S. Cronin.

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Doman, D.A., Cronin, D.S. & Salisbury, C.P. Characterization of Polyurethane Rubber at High Deformation Rates. Exp Mech 46, 367–376 (2006). https://doi.org/10.1007/s11340-006-6422-8

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  • High Strain Rate
  • Deformation Rate
  • Viscoelastic Model
  • Rubber Material
  • Uniaxial Compression Test