Skip to main content
SpringerLink
Log in

Modelling and numerical investigations of the mechanical behavior of polyurethane under the influence of moisture

  • Special
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In the present paper, a viscoelastic elastomer is investigated with respect to the influence of moisture on its mechanical behavior. Uniaxial relaxation tests are executed at room temperature with different levels of moisture content. The model consists of a finite viscoelastic and incompressible approach wherein the mechanical parameters are coupled to the moisture content. For numerical investigations, all necessary balance and constitutive equations are implemented in the open-source C++ finite element code deal.II (Bangerth et al. in ACM Trans Math Softw 33(4):24/1–24/27 2007). With the help of this implementation and by comparing experimental results for dry, intermediate and fully saturated specimens and the results gained from simulations, the precise material parameters of the used polymer can be identified.

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

Access this article

Log in via an institution

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

  1. Amin A., Lion A., Sekita S., Okui Y.: Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: Experimental identification and numerical verification. Int. J. Plast. 22(9), 1610–1657 (2006)

    Article  MATH  Google Scholar 

  2. Amin A., Lion A., Höfer P.: Effect of temperature history on the mechanical behaviour of a filler-reinforced nr/br blend: Literature review and critical experiments. Z. Angew. Math. Mech. 90(5), 347–369 (2010)

    Article  MATH  Google Scholar 

  3. Babuska I.: The finite element method for elliptic equations with discontinuous coefficients. Computing 5(3), 207–213 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bangerth W., Hartmann R., Kanschat G.: deal II – a general purpose object oriented finite element library. ACM Trans. Math. Softw. 33(4), 24/1–24/27 (2007)

    Article  MathSciNet  Google Scholar 

  5. Betten J.: Finite Elemente für Ingenieure 2: Variationsrechnung, Energiemethoden, Näherungsverfahren, Nichtlinearitäten, Numerische Integrationen. Springer, Berlin (1998)

    Book  Google Scholar 

  6. Björck A.: Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics, Philadelphia (1996)

    Book  MATH  Google Scholar 

  7. Braess D.: Finite Elemente: Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie. Springer, Berlin (1997)

    Book  Google Scholar 

  8. Brezzi F.: On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers. Rev. Fr. Autom. Inf. Rech. Oper. 8, 129–151 (1974)

    MathSciNet  MATH  Google Scholar 

  9. Coleman B., Gurtin M.: Thermodynamics with internal state variables. J. Chem. Phys. 47(2), 597–613 (1967)

    Article  Google Scholar 

  10. Coleman B., Noll W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13(1), 167–178 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  11. Cormen T., Leiserson C., Rivest R., Stein C.: Introduction to Algorithms. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  12. Crank J., Nicolson P.: A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Adv. Comput. Math. 6(1), 207–226 (1996)

    Article  MathSciNet  Google Scholar 

  13. Engelhard M., Lion A.: Modelling the hydrothermomechanical properties of polymers close to glass transition. Z. Angew. Math. Mech. 93(2-3), 102–112 (2013)

    Article  MathSciNet  Google Scholar 

  14. Greiner R., Schwarzl F.: Volume relaxation and physical aging of amorphous polymers I. theory of volume relaxation after single temperature jumps. Colloid. Polym. Sci. 267(1), 39–47 (1989)

    Article  Google Scholar 

  15. Haupt P.: Continuum Mechanics and Theory of Materials. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  16. Haupt P., Lion A.: On finite linear viscoelasticity of incompressible isotropic materials. Acta Mech. 159(1-4), 87–124 (2002)

    Article  MATH  Google Scholar 

  17. Haupt P., Lion A., Backhaus E.: On the dynamic behaviour of polymers under finite strains: Constitutive modelling and identification of parameters. Int. J. Solids Struct. 37(26), 3633–3646 (2000)

    Article  MATH  Google Scholar 

  18. Johlitz M.: Experimentelle Untersuchung und theoretische Modellierung von Maßstabseffekten in Klebungen. Shaker Verlag, Herzogenrath (2008)

    Google Scholar 

  19. Johlitz M., Scharding D., Diebels S., Retka J., Lion A.: Modelling of thermo-viscoelastic material behaviour of polyurethane close to the glass transition temperature. Z. Angew. Math. Mech. 90(5), 387–398 (2010)

    Article  MATH  Google Scholar 

  20. Johlitz, M., Retka, J., Lion, A.: Chemical ageing of elastomers: Experiments and modelling. ECCMR 2012 pp 113–118 (2012)

  21. Koprowski-Theiß N., Johlitz M., Diebels S.: Modelling of a cellular rubber with nonlinear viscosity functions. Exp. Mech. 51(5), 749–765 (2011)

    Article  Google Scholar 

  22. Ladyzhenskaya O.A.: The mathematical theory of viscous incompressible flow. Gordon and Breach, New York (1969)

    MATH  Google Scholar 

  23. Lion A., Johlitz M.: On the representation of chemical ageing of rubber in continuum mechanics. Int. J. Solids Struct. 49(10), 1227–1240 (2012)

    Article  MathSciNet  Google Scholar 

  24. Lion A., Peters J., Kolmeder S.: Simulation of temperature history-dependent phenomena of glass-forming materials based on thermodynamics with internal state variables. Thermochim. Acta 522(1-2), 182–193 (2011)

    Article  Google Scholar 

  25. Reese S., Govindjee S.: A theory of finite viscoelasticity and numerical aspects. Int. J. Solids Struct. 35(26-27), 3455–3480 (1998)

    Article  MATH  Google Scholar 

  26. Schäfer S.: Numerik im Maschinenbau. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  27. Schwarz, H.R.: Methode der finiten Elemente. Teubner Studienbücher, Stuttgart (1980)

  28. Steinbuch R.: Finite Elemente - Ein Einstieg. Springer, Berlin (1998)

    Book  MATH  Google Scholar 

  29. Taylor C., Hood P.: A numerical solution of the Navier-Stokes equations using the finite element technique. Comput. Fluids 1(1), 73–100 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  30. Tobolsky A.V.: Mechanische Eigenschaften und Struktur von Polymeren. Berliner Union, Stuttgart (1967)

    Google Scholar 

  31. Tortora M., Gorrasi G., Vittoria V., Galli G., Ritrovati S., Chiellini E.: Structural characterization and transport properties of organically modified montmorillonite/polyurethane nanocomposites. Polymer 43(23), 6147–6157 (2002)

    Article  Google Scholar 

  32. Yeoh O.: Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66(5), 754–771 (1993)

    Article  Google Scholar 

  33. Yeoh O., Fleming P.: A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity. J. Polym. Sci. Part B Polym. Phys. 35(12), 1919–1931 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Technische Mechanik, Universität des Saarlandes, Saarbrücken, Germany

    Florian Goldschmidt & Stefan Diebels

Authors
  1. Florian Goldschmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Diebels
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Florian Goldschmidt.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Goldschmidt, F., Diebels, S. Modelling and numerical investigations of the mechanical behavior of polyurethane under the influence of moisture. Arch Appl Mech 85, 1035–1042 (2015). https://doi.org/10.1007/s00419-014-0943-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-014-0943-x

Keywords

Search

Navigation