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The influence of viscosity on the response of open-cell polymeric foams in uniaxial compression: experiments and theoretical model

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Abstract

In a preceding paper (Pampolini and Del Piero in J Mech Mater Struct 3:969–981, 2008), the response of blocks made of a polymeric open-cell foam subject to uniaxial compression was analyzed. The hysteretic behavior exhibited in cyclic tests was interpreted within the context of nonlinear elasticity, as an effect of strain localization due to the non-convexity of the energy. Here we study some inelastic aspects of the response, such as rate dependence, strength decay after repeated loading, and memory effects. The analysis of some key experiments led us to the conclusion that viscous effects prevail over plasticity and damage. Consequently, we propose here a visco-elastic model, obtained by adding linear visco-elastic elements to our previous chain of nonlinear elastic springs. The paper is completed by the description of a series of experiments and of numerical simulations.

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References

  1. Amin A.F.M.S., 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. Plasticity 22, 1610–1657 (2006)

    Article  MATH  Google Scholar 

  2. Bardenhagen S.G., Brydon A.D., Guilkey J.E.: Insight into the physics of foam densification via numerical. Simulation. J. Mech. Phys. Solids 53, 597–617 (2005)

    Article  ADS  MATH  Google Scholar 

  3. Beatty M.F., Krishnaswamy S.: A theory of stress-softening in incompressible isotropic materials. J. Mech. Phys. Solids 48, 1931–1965 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Besdo D., Ihlemann J.: Properties of rubberlike materials under large deformations explained by self-organizing linkage patterns. Int. J. Plasticity 19, 1001–1018 (2003)

    Article  MATH  Google Scholar 

  5. Bueche F.: Mullins effect and rubber-filler interaction. J. Appl. Polymer Sci. 15, 271–281 (1961)

    Article  Google Scholar 

  6. DeSouza Neto E.A., Perić D., Owen D.R.: A phenomenological three-dimensional rate-indipendent continuum damage model for highly filled polymers: formulation and computational aspects. J. Mech. Phys. Solids 42, 1533–1550 (1994)

    Article  ADS  Google Scholar 

  7. De Tommasi D., Puglisi G., Saccomandi G.: A micromechanics-based model for the Mullins effect. J. Rheol. 50, 495–512 (2006)

    Article  ADS  Google Scholar 

  8. Dorfmann A., Ogden R.W.: A pseudo-elastic model for loading, partial unloading and reloading of particle-reinforced rubber. Int. J. Solids Struct. 40, 2699–2714 (2003)

    Article  MATH  Google Scholar 

  9. Drozdov A.D., Dorfmann A.: A micro-mechanical model for the response of filled elastomers at finite strains. Int. J. Plasticity 19, 1037–1067 (2003)

    Article  MATH  Google Scholar 

  10. Ericksen J.L.: Equilibrium of bars. J. Elast. 5, 191–201 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gibson L.J., Ashby M.F.: Cellular Solids: Structure and Properties. 2nd edn. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  12. Gioia G., Wang Y., Cuitiño A.M.: The energetics of heterogeneous deformation in open-cell solid foams. Proc. R. Soc. Lond. A 457, 1079–1096 (2001)

    Article  ADS  MATH  Google Scholar 

  13. Gong L., Kyriakides S.: Compressive response of open-cell foams. Part II: initiation and evolution of crushing. Int. J. Solids Struct. 42, 1381–1399 (2005)

    Article  MATH  Google Scholar 

  14. 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, 3633–3646 (2000)

    Article  MATH  Google Scholar 

  15. Jang W.-Y., Kraynik A.M., Kyriakides S.: On the microstructure of open-cell foams and its effect on elastic properties. Int. J. Solids Struct. 45, 1845–1875 (2008)

    Article  MATH  Google Scholar 

  16. Koeller R.C.: Applications of fractional calculus to the theory of viscoelasticity. ASME J. Appl. Mech. 51, 299–307 (1984)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Lakes R., Rosakis P., Ruina A.: Microbuckling instability in elastomeric cellular solids. J. Mater. Sci. 28, 4667–4672 (1993)

    Article  ADS  Google Scholar 

  18. Laroussi M., Sab K., Alaoui A.: Foam mechanics: nonlinear response of an elastic 3D-periodic microstructure. Int. J. Solids Struct. 39, 3599–3623 (2002)

    Article  MATH  Google Scholar 

  19. Lion A.: A constitutive model for carbon black filled rubber. Experimental investigations and mathematical representations. Continuum Mech. Thermodyn. 8, 153–169 (1996)

    Article  ADS  Google Scholar 

  20. Markert B.: A biphasic continuum approach for viscoelastic high-porosity foams: comprehensive theory, numerics, and applications. Arch. Comput. Methods Eng. 15, 371–446 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Miehe C., Keck J.: Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation. J. Mech. Phys. Solids 48, 323–365 (2000)

    Article  ADS  MATH  Google Scholar 

  22. Mullins L., Tobin N.R.: Theoretical model for the elastic behavior of filler-reinforced vulcanized rubbers. Rubber Chem. Technol. 30, 555–571 (1957)

    Article  Google Scholar 

  23. Ogden R.W., Roxburg D.G.: A pseudo-elastic model for the Mullins effect in filled rubber. Proc. R. Soc. Lond. A 455, 2861–2877 (1999)

    Article  ADS  MATH  Google Scholar 

  24. Pampolini G., Del Piero G.: Strain localization in open-cell polyurethane foams: experiments and theoretical model. J. Mech. Mater. Struct. 3, 969–981 (2008)

    Article  Google Scholar 

  25. Pampolini, G., Raous, M.: Non linear elasticity, viscosity and damage for polymeric foams (2011, submitted)

  26. Roberts A.P., Garboczi E.J.: Elastic properties of model random three-dimensional open-cell solids. J. Mech. Phys. Solids 50, 33–55 (2002)

    Article  ADS  MATH  Google Scholar 

  27. Sorrentino L., Aurelia M., Iannace S.: A simple method to predict high strain rates mechanical behavior of low interconnected cell foams. Polym. Test. 26, 878–885 (2000)

    Article  Google Scholar 

  28. Wang Y., Cuitiño A.N.: Full-field measurements of heterogeneous deformation patterns on polymeric foams using digital image correlation. Int. J. Solids Struct. 39, 3777–3796 (2002)

    Article  Google Scholar 

  29. Warren W.E., Kraynik A.M.: Linear elastic behavior of a low-density Kelvin foam with open cells. ASME J. Appl. Mech. 64, 787–793 (1997)

    Article  ADS  MATH  Google Scholar 

  30. White S.W., Kim S.K., Bajaj A.K., Davis P.: Experimental techniques and identification of nonlinear and viscoelastic properties of flexible polyurethane foam. Nonlinear Dyn. 22, 281–313 (2000)

    Article  MATH  Google Scholar 

  31. Zhu H.X., Mills N.J., Knott J.F.: Analysis of the high strain compression of open-cell foams. J. Mech. Phys. Solids 45, 1875–1904 (1997)

    Article  ADS  MATH  Google Scholar 

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Correspondence to Giampiero Pampolini.

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Communicated by Andreas Öchsner.

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Del Piero, G., Pampolini, G. The influence of viscosity on the response of open-cell polymeric foams in uniaxial compression: experiments and theoretical model. Continuum Mech. Thermodyn. 24, 181–199 (2012). https://doi.org/10.1007/s00161-011-0230-9

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  • DOI: https://doi.org/10.1007/s00161-011-0230-9

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