Identification of Rabotnov nonlinear constitutive relationship on the data of polyethylene and polypropylene creep tests

Deformable body mechanics


Stetsenko N. S.1*, Khokhlov A. V.2**

1. Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russia
2. Institute of Mechanics Lomonosov Moscow State University, 1, Michurinsky prospect, Moscow, 119192, Russia



The paper presents calibration technique for the Rabotnov nonlinear (quasi-linear) constitutive equation is developed using a set of creep curves of the material under uni-axial loading. The constitutive equation describes rheonomic materials behavior and generalizes the linear integral relationship of viscoelasticity with an arbitrary creep function by introducing the second material function. We propose to construct isochronous creep curves by the test data, approximate them by a number of special families of functions depending on 4-7 parameters and sel ect the most suitable family (the one yielding the smallest value of the relative quadratic deviation from the experimental points). As a rule, such families of functions could be chosen, which permit the analytic inversion of the constitutive equation, which enable not to resort to an approximate treatment procedure and reduce the identification error. Next, a “basic” isochronous curve should be selected (its selection is related to the choice of the characteristic time scale for the test under study). A nonlinearity function is being found fr om it. Then, with account for the specific features of the experimental data, the type of the creep function approximation is selected, and its parameters are found (using the nonlinearity function obtained before). The advantages of the identification technique were considered compared to the conventional one. In particular, the procedure for quantitative estimation of the similarity condition fulfillment for experimental isochronous creep curves (the necessary condition for the relation applicability) was proposed.

The identification procedure was applied to polyethylene and polypropylene creep tests. High-density polyethylene is widely used for manufacturing of water and gas supply pipes and other products. Thus, the study of their mechanical characteristics and their behavior modeling is of great interest. Verification of the obtained material functions was performed using the creep curves, that were not used for the identification procedure, stress-strain curves with constant rate and multi-step creep tests. It was shown, that the technique developed herein describes the experimental data well.


viscoelasticity, physical non-linearity, creep, identification, verification, polyethylene, polypropylene, polymers


  1. Rabotnov Yu.N. Prikladnaya matematika i mekhanika, 1948, vol. 12, no. 1, pp. 53 - 62.

  2. Namestnikov V.S., Rabotnov Yu.N. Prikladnaya mekhanika i tekhnicheskaya fizika, 1961, vol. 2, no. 4, pp. 148 - 150.

  3. Rabotnov Yu.N. Polzuchest' elementov konstruktsii (Creep of structural elements), Moscow, Nauka, 1966, 752 p.

  4. Rabotnov Yu.N., Papernik L.Kh., Stepanychev E.I. Mekhanika polimerov, 1971, no. 1, pp. 74 - 87.

  5. Rabotnov Yu.N., Papernik L.Kh., Stepanychev E.I. Mekhanika polimerov, 1971, no. 4, pp. 624 - 628.

  6. Dergunov N.N., Papernik L.Kh., Rabotnov Yu.N. Prikladnaya mekhanika i tekhnicheskaya fizika, 1971, no. 2, pp. 76 - 82.

  7. Rabotnov Yu.N., Suvorova Yu.V. Izvestiya AN SSSR. Mekhanika tverdogo tela, 1972, no. 4, pp. 41 - 54.

  8. Rabotnov Yu.N. Elementy nasledstvennoi mekhaniki tverdykh tel (Elements of hereditary mechanics of solids), Moscow, Nauka, 1977, 384 p.

  9. Suvorova Yu.V. Izvestiya AN SSSR. Mekhanika tverdogo tela, 2004, no. 1, pp. 174 - 181.

  10. Alekseeva S.I., Fronya M.A., Viktorova I.V. Kompozity i nanostruktury, 2011, no. 2, pp. 28 - 39.

  11. Fung Y.C. Stress-strain history relations of soft tissues in simple elongation. In: Biomechanics, Its Foundations and Objectives (ed. by Fung Y.C. et al.). New Jersey, Prentice-Hall, 1972, pp. 181 – 208.

  12. Fung Y.C. Biomechanics. Mechanical properties of living tissues, N.-Y, Springer-Verlag, 1993, 568 p.

  13. Funk J.R., Hall G.W., Crandall J.R., Pilkey W.D. Linear and quasi-linear viscoelastic characterization of ankle ligaments, Journal of Biomechanical Engineering, 2000, vol. 122, pp. 15 – 22.

  14. Nekouzadeh A., Pryse K.M., Elson E.L., Genin G.M. A simplified approach to quasi-linear viscoelastic modeling, Journal of Biomechanics, 2007, vol. 40, no. 14, pp. 3070 - 3078.

  15. De Frate L.E., Li G.The prediction of stress-relaxation of ligaments and tendons using the quasi-linear viscoelastic model, Biomechanics and Modeling in Mechanobiology, 2007, vol. 6, no. 4, pp. 245 - 251.

  16. Lakes R.S. Viscoelastic Materials, Cambridge, Cambridge University Press, 2009, 461 p.

  17. De Pascalis R., Abrahams I.D., Parnell W.J. On nonlinear viscoelastic deformations: a reappraisal of Fung’s quasi-linear viscoelastic model, Proceedings of the Royal Society A, 2014, V.470, 20140058. doi: 10.1098/rspa.2014.0058.

  18. Khokhlov A.V. Problemy prochnosti i plastichnosti, 2016, vol. 78, no. 4, pp. 452 - 466.

  19. Khokhlov A.V. Vestnik Moskovskogo universiteta. Matematika. Mekhanika, 2017, no. 5, pp. 26 - 31.

  20. Khokhlov A.V. Vestnik MGTU im. N.E. Baumana. Estestvennye nauki, 2017, no. 3, pp. 93 - 123.

  21. Khokhlov A.V. Mekhanika kompozitnykh materialov, 2018, vol. 54, no. 4, pp. 687 – 708,

  22. Khokhlov A.V. Izvestiya Rossiyskoy Akademii Nauk, Mekhanika tverdogo tela, 2018, no. 6. (in press).

  23. Khokhlov A.V. Trudy MAI, 2016, no. 91, available at:

  24. Khokhlov A.V. Izvestiya RAN. Mekhanika tverdogo tela, 2018, no. 3, pp. 81 - 104.

  25. Khokhlov A.V. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Fiziko-matematicheskie nauki, 2018, vol. 22, no. 1, pp. 1 - 31, doi: 10.14498/vsgtu1543

  26. Liu H., Polak M.A., Penlidis A. A practical approach to modeling time-dependent nonlinear creep behavior of polyethylene for structural applications, Polymer Engineering & Science, 2008, vol. 48, pp. 159 - 167.

  27. Kucher N.K., Zemtsov M.P., Danil'chuk E.L. Problemy prochnosti, 2007, no. 6, pp. 77 - 90.

  28. Popelar C.F., Popelar C.H., Kenner V.H. Viscoelastic material characterization and modeling for polyethylene, Polymer Engineering & Science, 1990, vol. 30, pp. 577 - 586.

  29. Lai J., Bakker A. Analysis of non-linear creep of high-density polyethylene, Polymer, 1995, vol. 36 (1), pp. 93 - 99.

  30. Zhang C., Moore I.D. Nonlinear mechanical response of high density polyethylene Part I experimental investigation and model evaluation, Polymer Engineering & Science, 1997, vol. 37, pp. 404 – 413.

  31. Hıllmansen S., Hobeika S., Haward R.N., Aleevers S. The effect of strain rate, temperature and molecular mass on the tensile deformation of polyethylene, Polymer Engineering & Science, 2000, vol. 40, pp. 481 – 489.

  32. Bonner M., Duckett R.A., Ward M.I. The creep behavior of isotropic polyethylene, Journal of Material Science, 1999, vol. 34, pp. 1885 – 1897.

  33. Dusunceli N., Colak O.U. The effects of manufacturing techniques on viscoelastic and viscoplastic behavior of high density polyethylene (HDPE), Materials and Design, 2008, vol. 29, pp. 1117 – 1124.

  34. Mizuno M., Sanomura Y. Phenomenological formulation of viscoplastic constitutive equation for polyethylene by taking into account strain recovery during unloading, Acta Mechanica, 2009, vol. 207, no. 1, pp. 83 - 93.

  35. Alekseev V.A., Karabin A.E. Trudy MAI, 2011, no. 49, available at:

  36. Kuleznev V.N., Ivanov M.S. Vysokomolekulyarnye soedineniya, 2016, vol. 58, no. 4, pp. 337 - 344.

  37. Ivanov M.S., Kuleznev V.N. Trudy VIAM, 2016, vol. 47, no. 11, pp. 68 - 77. Doi: 10.18577/2307-6046-2016-0-11-9-9

  38. Kuhl A., Munoz-Rojas P., Munoz-Rojas A., Barbieri R., Benvenutti I.J. A procedure for modeling the nonlinear viscoelastoplastic creep of HDPE at small strains, Polymer engineering and science, 2017, vol. 57, pp. 144 - 152.

  39. Bergstrom J.S. Mechanics of Solid Polymers. Theory and computational modeling, Elsevier, William Andrew, 2015, 520 p.

  40. Shesterikov S.A., Yumasheva M.A. Izvestiya AN SSSR. Mekhanika tverdogo tela, 1984, no. 1, pp. 86 - 91.

  41. Khokhlov A.V. Problemy prochnosti i plastichnosti, 2014, vol. 76, no. 4, pp. 343 - 356.

Download — informational site MAI

Copyright © 2000-2021 by MAI