Skip to main content
Log in

An Assessment of Nonlinearly Viscoelastic Constitutive Models for Cyclic Loading: The Effect of a General Loading/Unloading Rule

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

Predicting the unloading and/or cyclic deformation behavior of polymers is a challenge for most nonlinear viscoelastic constitutive models. Experimental data of an epoxy polymer under uniaxial loading/unloading and two other types of cyclic loadings are used to assess the predictive capabilities of three types of nonlinear viscoelastic models. A general loading/unloading criterion and a switching rule, proposed recently by the authors, are further modified and incorporated into each of the three models. For each model, predictions by both the original formulations and that incorporating the proposed loading/unloading rule are compared with the test data. It is clearly shown that such a rule is essential to correctly simulate the unloading and cyclic loading behavior of polymers. By introducing such a rule to constitutive models, the quantitative predictions can be improved, to various degrees of success, with respect to cyclic deformation features such as ratcheting under cyclic loading with a mean stress and stress relaxation under cyclic straining with a mean strain.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Arzoumanidis, G.A. and Liechti, K.M., ‘Linear viscoelastic property measurement and its significance for some nonlinear viscoelasticity models,’ Mech. Time-Depend. Mater., 7, 2003, 209–250.

    Article  ADS  Google Scholar 

  • Bardella, L., ‘A phenomenological constitutive law for the nonlinear viscoelastic behavior of epoxy resins in the glassy state,’ Eur. J. Mech. A/Solids 20, 2001, 907–924.

    Article  MATH  Google Scholar 

  • Brusselle-Dupend, N., Lai, D., Feaugas, X., Guigon, M. and Clavel, M., ‘Mechanical behavior of a semicrystalline polymer before necking. Part II: Modeling of uniaxial behavior,’ Polym. Eng. Sci. 43, 2003, 501–518.

    Article  Google Scholar 

  • Ellyin, F., Fatigue Damage, Crack Growth, and Life Prediction, Chapman & Hall, London, 1997, 179–204.

  • Hu, Y., Xia, Z. and Ellyin, F., ‘Deformation behavior of an epoxy resin subjected to multiaxial loadings, Part I: Experimental investigations,’ Polym. Eng. Sci. 43, 2003, 721–733.

    Article  Google Scholar 

  • Knauss, W.G. and Emri, I., ‘Nonlinear viscoelasticity based on free volume considerations,’ Computers & Structures, 13, 1981, 123–128.

    Article  MATH  Google Scholar 

  • Knauss, W.G. and Emri, I., ‘Volume change and the nonlinearly thermo-viscoelastic constitution of polymers,’ Polym. Eng. Sci., 27, 1987, 86–100.

    Article  Google Scholar 

  • Krempl, E. and Bordonaro, C.M., ‘A state variable model for high strength polymers,’ Polym. Eng. Sci., 35, 1995, 310–316.

    Article  Google Scholar 

  • Krishnaswamy, P., Tuttle, M.E. and Emery, A.F., ‘Finite-element modeling of the time-dependent behavior of nonlinear ductile polymers,’ Polym. Eng. Sci. 32, 1992, 1086–1096.

    Article  Google Scholar 

  • Lai, J. and Bakker, A., ‘Analysis of the non-linear creep of high-density polyethylene,’ Polymer 36, 1995, 93–99.

    Article  Google Scholar 

  • Lai, J. and Bakker, A., ‘3-D Schapery representation for nonlinear viscoelasticity and finite element implementation,’ Comput. Mech. 18, 1996, 182–191.

    Article  MATH  Google Scholar 

  • Losi, G.U. and Knauss, W.G., ‘Free volume theory and nonlinear thermoviscoelastictity,’ Polymer Eng. Sci. 32, 1992, 542–557.

    Article  Google Scholar 

  • Lustig, S.R. Shay, R.M. and Caruthers, J.M., ‘Thermodynamics constitutive equations for materials with memory on a material time scale,’ J. Rheol. 40, 1996, 69–106.

    Article  ADS  MathSciNet  Google Scholar 

  • Mlekusch, B., ‘Calculation of residual stress development in injection moulding using a nonlinear viscoelastic model,’ Mech. Time-Depend. Mat. 5, 2001, 101–118.

    Article  Google Scholar 

  • Popelar, C.F. and Liechti, K.M., ‘A distortion-modified free volume theory for nonlinear viscoelastic behavior,’ Mech. Time-Depend. Mat. 7, 2003, 89–141.

    Article  ADS  Google Scholar 

  • Popelar, C.F., Popelar, C.H. and Kenner, V.H., ‘Viscoelastic material characterization and modeling for polyethylene,’ Polym. Eng. Sci. 30, 1990, 577–586.

    Article  Google Scholar 

  • Schapery, R.A., ‘Nonlinear viscoelastic solids,’ Int. J. Solids & Structures 37, 2000, 359–366.

    Article  MATH  MathSciNet  Google Scholar 

  • Schapery, R.A., ‘On the characterization of nonlinear viscoelastic materials,’ Polym. Eng. Sci. 9, 1969, 295–310.

    Article  Google Scholar 

  • Shen, X., Xia, Z. and Ellyin, F., ‘Cyclic deformation of an epoxy polymer. Part I: Experimental investigation,’ Polym. Eng. Sci., 44, 2004, 2240–2246.

    Article  Google Scholar 

  • Stassi-D'Alia, F., ‘Limiting conditions of yielding for anisotropic materials,’ Meccanica 4, 1969, 349–364.

    Article  Google Scholar 

  • Weitsman, Y., ‘A continuum diffusion model for viscoelastic materials,’ J. Phys. Chem. 94, 1990, 961–968.

    Article  Google Scholar 

  • Xia, Z., Hu, Y. and Ellyin, F., ‘Deformation behavior of an epoxy resin subject to multiaxial loadings. Part II: Constitutive modeling and predictions,’ Polym. Eng. Sci. 43, 2003, 734–748.

    Article  Google Scholar 

  • Xia, Z., Shen, X. and Ellyin, F., ‘Cyclic deformation of an epoxy polymer. Part II: Predictions of viscoelastic constitutive models, Polym. Eng. Sci. 45, 2005, 103–113.

    Article  Google Scholar 

  • Xia, Z., Shen X. and Ellyin, F., ‘Biaxial cyclic deformation of an epoxy resin: Experiments and constitutive modeling,’ J. Mater. Sci. 40 2005, 643–654.

    Article  Google Scholar 

  • Zhang, C.T. and Moore, I.D., ‘Nonlinear mechanical response of high density polyethylene. Part I: Experimental investigation and model evaluation,’ Polym. Eng. Sci. 37 1997a, 404–413.

    Article  Google Scholar 

  • Zhang, C.T. and Moore, I.D., ‘Nonlinear mechanical response of high density polyethylene. Part II: Uniaxial constitutive modeling,’ Polym. Eng. Sci. 37 1997b, 414–420.

    Article  Google Scholar 

  • Zienkiewicz, O.C., Watson, M. and King, I.P., ‘A numerical method of viscoelastic stress analysis,’ Int. J. Mech. Sci. 10 1968, 807–827.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zihui Xia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xia, Z., Shen, X. & Ellyin, F. An Assessment of Nonlinearly Viscoelastic Constitutive Models for Cyclic Loading: The Effect of a General Loading/Unloading Rule. Mech Time-Depend Mater 9, 79–98 (2005). https://doi.org/10.1007/s11043-006-9004-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-006-9004-3

Keywords

Navigation