Non Linear Viscoelastic Constitutive Relation of Elastomers for Hysteresis Behavior

히스테리시스 거동을 하는 탄성체의 비선형 점탄성 구성방정식

  • Yoo, Sairom (Dept. of Aerospace Engineering, Korea Aerospace Univ.) ;
  • Ju, Jaehyung (Dept. of Mechanical Engineering, Univ. of North Texas) ;
  • Choi, Seok-Ju (R&D Center, Hnakook Tire Co. Ltd.) ;
  • Kim, Dooman (Dept. of Aerospace Engineering, Korea Aerospace Univ.)
  • Received : 2015.10.05
  • Accepted : 2016.02.10
  • Published : 2016.04.01


An accurate hysteresis model of an elastomer is important for quantifying viscoelastic energy loss. We suggest a highly nonlinear hyper-viscoelastic constitutive model of elastomers. The model captures a nonlinear viscoelastic characteristic by combining Yeoh's hyperelastic model and Hoofatt's hysteresis model used Neo-Hookean hyperelastic model. Analytical and numerical models were generated from uniaxial cyclic tests of an elastomer under a sinusoidal load with a mean strain of 150%, amplitudes of 20~80%, and frequencies of 0.02~0.2Hz. The viscoelastic model can highly capture the viscoelastic energy loss up to a strain of 230%.


Viscoelastic;Non-linear;Hyperelastic;Constitutive Relation


  1. Buckley, Mc C. and Bucknell, 2003, Principles of Polymer Engineering, pp. 117-176.
  2. Wiechert, E., 1889, Ueber Elastische Nachwirkung, Dissertation, Konigsberg University, Germany.
  3. Wiechert, E., 1893, Gesetze der elastischen Nachwirkung fur constante Temperatur, Annalen der Physik, pp. 286, 335-348, 546-570.
  4. Soussou, J. E., Moavenzadeh, F. and Gradowczyk, M. H., 1970, "Application of Prony Series to Linear Viscoelasticity," Trans. Soc. Rheol. Vol. 14, pp. 573-584.
  5. Haupt, P. and Lion, A., 2002, "On Finite Linear Viscoelasticity of Incompressible Isotropic Materials," Acta Mech. Vol. 159, pp. 87-124.
  6. Bergstrom, J. S. and Boyce, M. C., 1998, "Constitutive Modeling of the Large Strain Time-dependent Behavior of Elastomers," J. Mech. Phys. Solids, Vol. 46, pp. 931-954.
  7. Bergstrom, J. S. and Boyce, M. C., 2001, "Constitutive Modeling of the Time-dependent and Cyclic Loading of Elastomers and Application to Soft Biological Tissues," Mech. Mater, Vol. 33, pp. 523-530.
  8. Lion, A., 1996, "A Constitutive Model for Carbon Black Filled Rubber: Experimental Investigations and Mathematical Representation," Continuum Mech. Thermo-dyna, Vol. 8 pp. 153-169.
  9. Lion, A., 1997, "A Physically Based Method to Represent the Thermo-mechanical Behavior of Elastomers," Acta Mech. Vol. 123, pp. 1-25.
  10. Tomita, Y., Lu, W., Naito, M. and Furutani, Y., 2006, "Numerical Evaluation of Micro - to Macroscopic Mechanical Behavior of Carbon-black-filled Rubber," International Journal of Mechanical Sciences, Vol. 48, pp. 108-116.
  11. Tomita, Y., Azuma, K. and Naito, M., 2008, "Computational Evaluation of Strain-rate-dependent Deformation Behavior of Rubber and Carbon-blackfilled Rubber Under Monotonic and Cyclic Straining," Int. J. Mech. Sci, Vol. 50 pp. 856-868.
  12. Liu, M. and HooFatt, Michelle S., 2011, "A Constitutive Equation for Filled Under Cyclic Loading," International Journal of Non-Linear Mechanics, Vol. 46, pp. 446-456.
  13. Liu, F., Sutcliffe, M.P.F. and Graham, W.R., 2010, "Prediction of Tread Block Forces for a Free-rolling Tyre in Contact with a Smooth Road," Wear, Vol. 269, pp. 672-683.
  14. Lee, E.H. and Liu, D.H., 1967, "Finite-strain Elastic-plastic Theory with Application to Plane-wave Analysis," J. Appl. Phys., Vol. 38 pp. 19-27.
  15. Huber, N., Tsakmakis, C., 2000, "Finite Deformation Viscoelasticity Laws," Mech. Mater., Vol. 32 pp. 1-18.
  16. Robertson, C. G. and Wang, X., 2006, "Spectral Hole Burning to Probe the Nature of Unjamming (Payne effect) in Particulate-filled Elastomers," Europhys. Lett, Vol. 76, pp. 278-284.
  17. Payne, A.R., 1967, "Dynamic properties of PBNA-natural Rubber Vulcanizates," J. Appl. Polym. Sci. Vol. 11, pp. 383-387.

Cited by

  1. Optimal Design for the Rear-Glass Joint of an Automobile for Squeak and Rattle Noise Reduction vol.19, pp.5, 2018,