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A microcell-based constitutive modeling of cellulose aerogels under tension

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Abstract

Cellulose aerogels are characterized by a cellular morphology. The mechanics of such materials is largely dictated by the behavior of their cell walls. Under tension, these aerogels undergo only small strains while their cell walls are subject to combined bending and tension loading. Accordingly, in the present paper, we describe the kinematics of these cell wall fibrils based on the Euler–Bernoulli beam theory. The microscopic damage criterion is based on the normal stress in the cell walls. Variation in the sizes of the microcells is accounted for by using the pore-size data from experiments. The so-resulting constitutive model includes few micromechanically motivated material parameters, shows very good agreement with our own experimental data of cellulose aerogels, and also accurately predicts material failure under tension.

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References

  1. Barrett, E.P., Joyner, L.G., Halenda, P.P.: The determination of pore volume and area distributions in porous substances. i. computations from nitrogen isotherms. J. Am. Chem. Soc. 73(1), 373–380 (1951)

    Article  Google Scholar 

  2. Bazant, Z.P., Oh, B.H.: Efficient numerical integration on the surface of a sphere. Z. Angew. Math. Mech. 66(1), 37–49 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brunauer, S., Emmett, P.H., Teller, E.: Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60(2), 309–319 (1938)

    Article  Google Scholar 

  4. Davini, C., Ongaro, F.: A homogenized model for honeycomb cellular materials. J. Elast. 104(1–2), 205–226 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Diebels, S., Ebinger, T., Steeb, H.: An anisotropic damage model of foams on the basis of a micromechanical description. J. Mater. Sci. 40(22), 5919–5924 (2005)

    Article  Google Scholar 

  6. Ehret, A.E., Itskov, M., Schmid, H.: Numerical integration on the sphere and its effect on the material symmetry of constitutive equations—a comparative study. Int. J. Numer. Methods Eng. 81, 189–189 (2009)

    MATH  Google Scholar 

  7. El Ghezal, M.I., Maalej, Y., Doghri, I.: Micromechanical models for porous and cellular materials in linear elasticity and viscoelasticity. Comput. Mater. Sci. 70, 51–70 (2013)

    Article  Google Scholar 

  8. Ford, C.M., Gibson, L.J.: Uniaxial strength asymmetry in cellular materials: an analytical model. Int. J. Mech. Sci. 40(6), 521–531 (1998)

    Article  MATH  Google Scholar 

  9. García-González, C.A., Alnaief, M., Smirnova, I.: Polysaccharide-based aerogels? Promising biodegradable carriers for drug delivery systems. Carbohydr. Polym. 86(4), 1425–1438 (2011)

    Article  Google Scholar 

  10. Gavillon, R., Budtova, T.: Aerocellulose: new highly porous cellulose prepared from cellulose-naoh aqueous solutions. Biomacromolecules 9, 269–277 (2008)

    Article  Google Scholar 

  11. Gibson, L.J.: Biomechanics of cellular solids. J. Biomech. 38(3), 377–99 (2005)

    Article  Google Scholar 

  12. Gibson, L.J., Ashby, M.F.: Cellular Solids: Structure and Properties. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  13. Heo, S., Xu, Y.: Constructing fully symmetric cubature formulae for the sphere. Math. Comput. 70(233), 269–279 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Itskov, M.: On the accuracy of numerical integration over the unit sphere applied to full network models. Comput. Mech. 57(5), 859–865 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  15. Jo, C., Fu, J., Naguib, H.E.: Constitutive modeling for mechanical behavior of pmma microcellular foams. Polymer 46(25), 11896–11903 (2005)

    Article  Google Scholar 

  16. Jung, A., Diebels, S.: Modelling of metal foams by a modified elastic law. Mech. Mater. 101, 61–70 (2016)

    Article  Google Scholar 

  17. Jung, A., Grammes, T., Diebels, S.: Micro-structural motivated phenomenological modelling of metal foams: experiments and modelling. Arch. Appl. Mech. 85(8), 1147–1160 (2014)

    Article  Google Scholar 

  18. Kistler, S.S.: Coherent expanded-aerogels. J. Phys. Chem. 36(1), 52–64 (1931)

    Article  Google Scholar 

  19. Liebner, F., Potthast, A., Rosenau, T., Haimer, E., Wendland, M.: Cellulose aerogels: highly porous, ultra-lightweight materials. Holzforschung 62(2), 129–135 (2008)

    Article  Google Scholar 

  20. Liu, P.S.: Mechanical behaviors of porous metals under biaxial tensile loads. Mater. Sci. Eng. A 422(1–2), 176–183 (2006)

    Article  Google Scholar 

  21. Mehling, T., Smirnova, I., Guenther, U., Neubert, R.H.H.: Polysaccharide-based aerogels as drug carriers. J. Non Cryst. Solids 355(50–51), 2472–2479 (2009)

    Article  Google Scholar 

  22. Onck, P.R., Koeman, T., van Dillen, T., van der Giessen, E.: Alternative explanation of stiffening in cross-linked semiflexible networks. Phys. Rev. Lett. 95(17), 178,102 (2005)

    Article  Google Scholar 

  23. Ratke, L.: Monoliths and Fibrous Cellulose Aerogels, pp. 173–190. Springer, New York (2011)

    Google Scholar 

  24. Rege, A., Schestakow, M., Karadagli, I., Ratke, L., Itskov, M.: Micro-mechanical modelling of cellulose aerogels from molten salt hydrates. Soft Matter 12(34), 7079–7088 (2016)

    Article  Google Scholar 

  25. Schestakow, M., Karadagli, I., Ratke, L.: Cellulose aerogels prepared from an aqueous zinc chloride salt hydrate melt. Carbohydr. Polym. 137, 642–649 (2016)

    Article  Google Scholar 

  26. Tannert, R., Schwan, M., Rege, A., Eggeler, M., da Silva, J.C., Bartsch, M., Milow, B., Itskov, M., Ratke, L.: The three-dimensional structure of flexible resorcinol-formaldehyde aerogels investigated by means of holotomography. J. Sol Gel Sci. Technol. (2017). https://doi.org/10.1007/s10971-017-4363-6

    Google Scholar 

  27. Triantafillou, T.C., Gibson, L.J.: Constitutive modeling of elastic–plastic open-cell foams. J. Eng. Mech. 116(12), 2772–2778 (1990)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Continuum Mechanics, RWTH Aachen University, Kackertstraße 9, 52072, Aachen, Germany

    Ameya Rege & Mikhail Itskov

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  1. Ameya Rege
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  2. Mikhail Itskov
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Correspondence to Ameya Rege.

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This paper is dedicated to the memory of Franz Ziegler

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Rege, A., Itskov, M. A microcell-based constitutive modeling of cellulose aerogels under tension. Acta Mech 229, 585–593 (2018). https://doi.org/10.1007/s00707-017-1987-0

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  • DOI: https://doi.org/10.1007/s00707-017-1987-0

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