Iranian Polymer Journal

, Volume 28, Issue 2, pp 135–144 | Cite as

A multi-scale three-dimensional finite element analysis of polymeric rubber foam reinforced by carbon nanotubes under tensile loads

  • Alireza Shojaei Dindarloo
  • Mohammad KarrabiEmail author
  • Mir Hamid Reza Ghoreishy
Original Research


A multi-scale FEM analysis was set up using two different unit cells to estimate the properties of a nanoparticle-reinforced rubber foam from the base material. Rubber foam was made up of EPDM rubber and reinforced by multiwall carbon nanotubes. This analysis was performed in two stages. In the first stage, the mechanical behavior of polymeric nanocomposite was predicted under uniaxial tension using the unit cell type I; in the second stage, the overall foam behavior was predicted by implementing the results of the first stage in unit cell type II as a constitutive material, with both cell types being in different dimensional scales. The polymeric material was assumed as an incompressible media and Ogden hyperelastic model was used as a material model. Both simulation stages incorporated unit cells as representative volume element and periodic boundary conditions. Polymeric material parameters for Ogden hyperelastic model were calculated using tensile testing of vulcanized pure EPDM. To validate the model, numerical analysis results were compared to experimental tensile tests of nanoparticle-reinforced foam, which was prepared with similar density and nanoparticle content as in the simulation. The foam porosity size and content of carbon nanotubes were adjustable in this study using unit cell parameters.


Rubber foam FEM Multi-scale 3D simulation Representative volume element MWCNT-reinforced foam 


  1. 1.
    Keramati M, Ghasemi I, Karrabi M, Azizi H (2012) Microcellular foaming of PP/EPDM/organoclay nanocomposites: the effect of the distribution of nanoclay on foam morphology. Polym J 44:433–438CrossRefGoogle Scholar
  2. 2.
    Gibson LJ, Ashby MF (1988) Cellular solids: structure and properties. Cambridge University, CambridgeGoogle Scholar
  3. 3.
    Li W, Jia H, Pu C, Liu X, Xie J (2015) Cell wall buckling mediated energy absorption in lotus-type porous copper. J Mater Sci Technol 31:1018–1026CrossRefGoogle Scholar
  4. 4.
    Thakur V, Li Pi Shan C, Li G, Han T, Den Doelder J (2018) Sponge EPDM by design. Plast Rubber Compos 47:1–10CrossRefGoogle Scholar
  5. 5.
    Plachy T, Kratina O, Sedlacik M (2018) Porous magnetic materials based on EPDM rubber filled with carbonyl iron particles. Compos Struct 192:126–130CrossRefGoogle Scholar
  6. 6.
    Tekog̃lu C, Gibson LJ, Pardoen T, Onck PR (2011) Size effects in foams: experiments and modeling. Prog Mater Sci 56:109–138CrossRefGoogle Scholar
  7. 7.
    Ghasemi I, Karrabi M, Mohammadi M, Azizi H (2010) Evaluating the effect of processing conditions and organoclay content on the properties of styrene-butadiene rubber/organoclay nanocomposites by response surface methodology. Express Polym Lett 4:62–70CrossRefGoogle Scholar
  8. 8.
    Shang S, Gan L, Yuen MC, Jiang S, Luo NM (2014) Carbon nanotubes based high temperature vulcanized silicone rubber nanocomposite with excellent elasticity and electrical properties. Compos Part A Appl Sci Manuf 66:135–141CrossRefGoogle Scholar
  9. 9.
    Bhattacharya M, Maiti M, Bhowmick AK (2009) Tailoring properties of styrene butadiene rubber nanocomposite by various nanofillers and their dispersion. Polym Eng Sci 49:81–98CrossRefGoogle Scholar
  10. 10.
    Chen L, Ozisik R, Schadler LS (2010) The influence of carbon nanotube aspect ratio on the foam morphology of MWNT/PMMA nanocomposite foams. Polymer 51:2368–2375CrossRefGoogle Scholar
  11. 11.
    Lee L, Zeng C, Cao X, Han X, Shen J, Xu G (2005) Polymer nanocomposite foams. Compos Sci Technol 65:2344–2363CrossRefGoogle Scholar
  12. 12.
    Goren K, Chen L, Schadler LS, Ozisik R (2010) Influence of nanoparticle surface chemistry and size on supercritical carbon dioxide processed nanocomposite foam morphology. J Supercrit Fluid 51:420–427CrossRefGoogle Scholar
  13. 13.
    Bazli L, Khavandi A, Boutorabi MA, Karrabi M (2017) Correlation between viscoelastic behavior and morphology of nanocomposites based on SR/EPDM blends compatibilized by maleic anhydride. Polymer 113:156–166CrossRefGoogle Scholar
  14. 14.
    Pardo-Alonso S, Solórzano E, Brabant L, Vanderniepen P, Dierick M, Van Hoorebeke L, Rodríguez-Pérez MA (2013) 3D Analysis of the progressive modification of the cellular architecture in polyurethane nanocomposite foams via X-ray microtomography. Eur Polym J 49:999–1006CrossRefGoogle Scholar
  15. 15.
    Dutta A, Ghosh AK (2018) Morphological and rheological footprints corroborating optimum foam processability of PP/ethylene acrylic elastomer blend. J Appl Polym Sci 135:1–12Google Scholar
  16. 16.
    Zhu H, Hobdell J, Windle A (2000) Effects of cell irregularity on the elastic properties of open-cell foams. Acta Mater 48:4893–4900CrossRefGoogle Scholar
  17. 17.
    Thiyagasundaram P, Sankar BV, Arakere NK (2010) Elastic properties of open-cell foams with tetrakaidecahedral cells using finite element analysis. AIAA J 48:818–828CrossRefGoogle Scholar
  18. 18.
    Irausquín I, Pérez-Castellanos JL, Miranda V, Teixeira-Dias F (2013) Evaluation of the effect of the strain rate on the compressive response of a closed-cell aluminium foam using the split Hopkinson pressure bar test. Mater Des 47:698–705CrossRefGoogle Scholar
  19. 19.
    Zhai W, Park CB, Kontopoulou M (2011) Nanosilica addition dramatically improves the cell morphology and expansion ratio of polypropylene heterophasic copolymer foams blown in continuous extrusion. Ind Eng Chem Res 50:7282–7289CrossRefGoogle Scholar
  20. 20.
    Raghunath R, Juhre D (2013) Finite element simulation of deformation behaviour of cellular rubber components. Mech Res Commun 47:32–38CrossRefGoogle Scholar
  21. 21.
    Sabuwala T, Gioia G (2013) Skeleton-and-bubble model of polyether–polyurethane elastic open-cell foams for finite element analysis at large deformations. J Mech Phys Solid 61:886–911CrossRefGoogle Scholar
  22. 22.
    Anani Y, Alizadeh Y (2011) Visco-hyperelastic constitutive law for modeling of foam’s behavior. Mater Des 32:2940–2948CrossRefGoogle Scholar
  23. 23.
    Treloar LRG (2005) The physics of rubber elasticity, 3rd edn. Oxford University, OxfordGoogle Scholar
  24. 24.
    Flügge W (1975) Viscoelasticity, 2nd edn. Springer, BerlinCrossRefGoogle Scholar
  25. 25.
    Rafiee R, Firouzbakht V (2014) Multi-scale modeling of carbon nanotube reinforced polymers using irregular tessellation technique. Int J Mech Mater 78:74–84CrossRefGoogle Scholar
  26. 26.
    Shokrieh MM, Rafiee R (2010) Stochastic multi-scale modeling of CNT/polymer composites. Comput Mater Sci 50:437–446CrossRefGoogle Scholar
  27. 27.
    Rafiee R, Ghorbanhosseini A (2017) Stochastic multi-scale modeling of randomly grown CNTs on carbon fiber. Mech Mater 106:1–7CrossRefGoogle Scholar
  28. 28.
    Shokrieh MM, Rafiee R (2012) Development of a full range multi-scale model to obtain elastic properties of CNT/polymer composites. Iran Polym J 21:397–402CrossRefGoogle Scholar
  29. 29.
    Alireza Shojaei D, Karrabi M, Ghoreishy MHR (2017) Effect of different types of nano-particles on the morphology and mechanical properties of EPDM foam. Cell Polym 36:113–134CrossRefGoogle Scholar
  30. 30.
    Matouš K, Geers MGD, Kouznetsova VG, Gillman A (2017) A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials. J Comput Phys 330:192–220CrossRefGoogle Scholar
  31. 31.
    Geers MGD, Kouznetsova VG, Matouš K, Yvonnet J (2017) Homogenization methods and multiscale modeling: nonlinear problems. Wiley, New YorkGoogle Scholar
  32. 32.
    Ogden RW, Saccomandi G, Sgura I (2004) Fitting hyperelastic models to experimental data. Comput Mech 34:484–502CrossRefGoogle Scholar
  33. 33.
    Qi HJ, Teo KBK, Lau KKS, Boyce MC, Milne WI, Robertson J, Gleason KK (2003) Determination of mechanical properties of carbon nanotubes and vertically aligned carbon nanotube forests using nanoindentation. J Mech Phys Solid 51:2213–2237CrossRefGoogle Scholar
  34. 34.
    Bazli L, Khavandi A (2016) Morphology and viscoelastic behavior of silicone rubber/EPDM/Cloisite 15A nanocomposites based on Maxwell model. Iran Polym J 25:907–918CrossRefGoogle Scholar
  35. 35.
    Simone AE, Gibson LJ (1998) Effects of solid distribution on the stiffness. Acta Mater 46:2139–2150CrossRefGoogle Scholar

Copyright information

© Iran Polymer and Petrochemical Institute 2019

Authors and Affiliations

  • Alireza Shojaei Dindarloo
    • 1
  • Mohammad Karrabi
    • 1
    Email author
  • Mir Hamid Reza Ghoreishy
    • 1
  1. 1.Iran Polymer and Petrochemical InstituteTehranIran

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