Strain Amplitude Effect on the Viscoelastic Mechanics of Chloroprene Rubber

  • Longfan PengEmail author
  • Zhida Li
  • Yunyu Li


This paper establishes an empirical formula to predict the strain amplitude effect. A viscoelastic constitutive model—the superposition of a hyperelastic model and a viscoelastic model—is constructed based on the laws of thermodynamics. The Mooney–Rivlin model and the Prony series are employed for uniaxial tension testing. The empirical formula is derived using a hysteresis loop; it obtains results that are in agreement with the experimental results of dynamic mechanical analysis (DMA). The empirical formula proposed in this paper has certain accuracy in predicting the dynamic modulus under different strain amplitudes.


Viscoelasticity Strain amplitude effect Storage modulus Loss modulus Hysteresis loop 



The project was financially supported by the National Natural Science Foundation of China (No. 51708433) and the Fundamental Research Funds. We would like to thank Editage ( for English language editing.


  1. 1.
    Dai W, Moroni MO, Roesset JM, et al. Effect of isolation pads and their stiffness on the dynamic characteristics of bridges. Eng Struct. 2006;28(9):1298–306.CrossRefGoogle Scholar
  2. 2.
    Siqueira GH, Tavares DH, Paultre P, et al. Performance evaluation of natural rubber seismic isolators as a retrofit measure for typical multi-span concrete bridges in eastern Canada. Eng Struct. 2014;74:300–10.CrossRefGoogle Scholar
  3. 3.
    Yuan Y, Wei W, Tan P, et al. A rate-dependent constitutive model of high damping rubber bearings: modeling and experimental verification. Earthq Eng Struct Dyn. 2016;45(11):1875–92.CrossRefGoogle Scholar
  4. 4.
    Xiang N, Li J. Experimental and numerical study on seismic sliding mechanism of laminated-rubber bearings. Eng Struct. 2017;141:159–74.CrossRefGoogle Scholar
  5. 5.
    Ahmadipour M, Alam MS. Sensitivity analysis on mechanical characteristics of lead-core steel-reinforced elastomeric bearings under cyclic loading. Eng Struct. 2017;140:39–50.CrossRefGoogle Scholar
  6. 6.
    Tinard V, Brinster M, Francois P, et al. Experimental assessment of sound velocity and bulk modulus in high damping rubber bearings under compressive loading. Polym Test. 2018;65:331–8.CrossRefGoogle Scholar
  7. 7.
    Mullins L. Effect of stretching on the properties of rubber. Rubber Chem Technol. 1948;21(2):281–300.CrossRefGoogle Scholar
  8. 8.
    Diani J, Brieu M, Batzler K, et al. Effect of the Mullins softening on mode I fracture of carbon-black filled rubbers. Int J Fract. 2015;194(1):11–8.CrossRefGoogle Scholar
  9. 9.
    Sokolov AK, Svistkov AL, Shadrin VV, et al. Influence of the Mullins effect on the stress-strain state of design at the example of calculation of deformation field in tyre. Int J Nonlinear Mech. 2018;104:67–74.CrossRefGoogle Scholar
  10. 10.
    Payne AR. The dynamic properties of carbon black—natural rubber vulcanizates. Part I. J Appl Polym Sci. 1963;6(19):57–63.CrossRefGoogle Scholar
  11. 11.
    Kraus G. Mechanical losses in carbon-black-filled rubbers. J Appl Polym Symp. 1984;39:75–92.Google Scholar
  12. 12.
    Luo W, Hu X, Wang C, et al. Frequency-and strain-amplitude-dependent dynamical mechanical properties and hysteresis loss of CB-filled vulcanized natural rubber. Int J Mech Sci. 2010;52(2):168–74.CrossRefGoogle Scholar
  13. 13.
    Lion A, Kardelky C, Haupt P. On the frequency and amplitude dependence of the Payne effect: theory and experiments. Rubber Chem Technol. 2003;76(2):533–47.CrossRefGoogle Scholar
  14. 14.
    Lion A, Kardelky C. The Payne effect in finite viscoelasticity: constitutive modelling based on fractional derivatives and intrinsic time scales. Int J Plast. 2004;20(7):1313–45.CrossRefGoogle Scholar
  15. 15.
    Hofer P, Lion A. Modelling of frequency- and amplitude-dependent material properties of filler-reinforced rubber. J Mech Phys Solids. 2009;57:500–20.CrossRefGoogle Scholar
  16. 16.
    Kim BK, Youn K. A viscoelastic constitutive model of rubber under small oscillatory load superimposed on large static deformation. Arch Appl Mech. 2001;71(11):748–63.CrossRefGoogle Scholar
  17. 17.
    Tomita Y, Azuma K, Naito M. Computational evaluation of strain-rate dependent deformation behavior of rubber and carbon-black-filled rubber under monotonic and cyclic straining. Int J Mech Sci. 2008;50:856–68.CrossRefGoogle Scholar
  18. 18.
    Kar KR, Bhowmick AK. Effect of holding time on high strain hysteresis loss of carbon black filled rubber vulcanizates. Polym Eng Sci. 1998;38(12):1927–45.CrossRefGoogle Scholar
  19. 19.
    Kar KK, Bhowmick AK. Medium strain hysteresis loss of natural rubber and styrene-butadiene rubber vulcanizates: a predictive model. Polymer. 1999;40(3):683–94.CrossRefGoogle Scholar
  20. 20.
    Park DM, Hong WH, Kim SG, et al. Heat generation of filled rubber vulcanizates and its relationship with vulcanizate network structures. Eur Polym J. 2000;36(11):2429–36.CrossRefGoogle Scholar
  21. 21.
    Ismail H, Osman H, Ariffin A. Curing characteristics, fatigue and hysteresis behaviour of feldspar filled natural rubber vulcanizates. J Macromol Sci Part D Rev Polym Process. 2007;46(6):6.Google Scholar
  22. 22.
    Yang R, Song Y, Zheng Q. Payne effect of silica-filled styrene-butadiene rubber. Polymer. 2017;116:304–13.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.Institute of TransportationWuhan University of TechnologyWuhanChina

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