Acta Mechanica

, Volume 205, Issue 1–4, pp 77–84 | Cite as

Effect of fiber orientation on the non-affine deformation of random fiber networks

Article

Abstract

The study of fiber networks is essential in understanding the mechanical properties of many polymeric and biological materials. These systems deform non-affinely, i.e. the local deformation is different than the applied far-field. The degree of non-affinity increases with decreasing scale of observation. Here, we show that this relationship is a power law with a scaling exponent independent of the type of applied load. Preferential fiber orientation influences non-affinity in a significant way: this parameter generally increases upon increasing orientation. However, some components of non-affinity, such as that associated with the normal strain in the direction of the preferential fiber orientation, decrease. In random networks, the nature of the far-field has little influence on the level of non-affinity. This is not the case in oriented networks.

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References

  1. 1.
    Janmey P.A.: Mechanical properties of cytoskeletal polymers. Curr. Opin. Cell Biol. 4, 4–11 (1991)CrossRefGoogle Scholar
  2. 2.
    Chandran P.L., Barocas V.H.: Affine versus non-affine fibril kinematics in collagen networks: theoretical studies of network behavior. J. Biomech. Eng. 128, 259–270 (2006)CrossRefGoogle Scholar
  3. 3.
    Wang C.W., Cheng X., Sastry A.M., Choi S.B.: Investigation of failure processes in porous battery substrates. Part I. Experimental findings. J. Eng. Mater. Technol. 121, 503–513 (1999)CrossRefGoogle Scholar
  4. 4.
    Alava M., Niskanen K.: The physics of paper. Rep. Prog. Phys. 69, 669–723 (2006)CrossRefGoogle Scholar
  5. 5.
    Ostoja-Starzewski M., Stahl D.C.: Random fiber networks and special elastic orthotropy of paper. J. Elast. 60, 131–149 (2000)MATHCrossRefGoogle Scholar
  6. 6.
    Kroy K., Frey E.: Force–extension relation and plateau modulus for wormlike chains. Phys. Rev. Lett. 77, 306–39 (1996)CrossRefGoogle Scholar
  7. 7.
    Wu X.F., Dzenis Y.A.: Elasticity of planar fiber networks. J. Appl. Phys. 98, 093501 (2005)CrossRefGoogle Scholar
  8. 8.
    Narter M.A., Barta S.K., Buchanan D.R.: Micromechanics of three-dimensional fiberwebs: constitutive equations. Proc. R. Soc. A 455, 3543–3563 (1998)CrossRefGoogle Scholar
  9. 9.
    Head D.A., Levine A.J., MacKintosh F.C.: Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks. Phys. Rev. E 68, 061907 (2003)CrossRefGoogle Scholar
  10. 10.
    Wilhelm J., Frey E.: Elasticity of stiff polymer networks. Phys. Rev. Lett. 91, 108103 (2003)CrossRefGoogle Scholar
  11. 11.
    Onck P.R., Koeman T., van Dillen T., vand der Giessen E.: Alternative explanation of stiffening in cross-linked semiflexible networks. Phys. Rev. Lett. 95, 178102 (2005)CrossRefGoogle Scholar
  12. 12.
    Hatami-Marbini H., Picu R.C.: Scaling of nonaffine deformation in random semiflexible fiber networks. Phys. Rev. E 77, 062103 (2008)CrossRefGoogle Scholar
  13. 13.
    Heussinger C., Frey E.: Stiff polymers, foams, and fiber networks. Phys. Rev. Lett. 96, 017802 (2006)CrossRefGoogle Scholar
  14. 14.
    DiDonna B.A., Lubensky T.C.: Nonaffine correlations in random elastic media. Phys. Rev. E 72, 066619 (2005)CrossRefGoogle Scholar
  15. 15.
    Langer S.A., Liu A.J.: Nonaffine correlations in random elastic media. J. Phys. Chem. B 101, 8667–8671 (1997)CrossRefGoogle Scholar
  16. 16.
    Head D.A., MacKintosh F.C., Levine A.J.: Nonuniversality of elastic exponents in random bond-bending networks. Phys. Rev. E 68, 025101 (2003)CrossRefGoogle Scholar
  17. 17.
    Leonforte F., Tanguy A., Wittmer J.P., Barrat J.L.: Continuum limit of amorphous elastic bodies. II. Linear response to a point source force. Phys. Rev. B 70, 014203 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical Aerospace and Nuclear EngineeringRensselaer Polytechnic InstituteTroyUSA

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