Skip to main content
SpringerLink
Log in

Long-range correlations of elastic fields in semi-flexible fiber networks

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

The mechanical properties of semi-flexible networks have been the subject of intense theoretical and experimental studies concerned primarily with the understanding of the complex behavior of biological systems such as the cell. Here it is shown that the elasticity of these networks, both elastic constants and elastic fields, while fluctuating significantly with position, is long-range correlated and the correlation functions exhibit power law scaling. The correlations are lost when the fiber stiffness is reduced. The range of scales over which correlations are observed is bounded below by the mean fiber segment length and above by the filament persistence length. Therefore, these networks can be regarded as stochastic fractal elastic media over the respective range of scales. This implies that no scale decoupling exists and no representative volume element can be identified on scales below the upper correlation cut-off scale.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Lodish H, Berk A, Matsudaira P, Kaiser CA, Krieger M, Scott MP, Zipursky L, Darnell J (2001) Molecular cell biology. Freeman, New York

    Google Scholar 

  2. Stossel TP (1994) The machinery of cell crawling. Sci Am 271: 54–63

    Article  Google Scholar 

  3. Chaudhuri O, Parekh SH, Fletcher DA (2007) Reversible stress softening of actin networks. Nature 445: 295–298

    Article  Google Scholar 

  4. Janmey PA, McCormick ME, Rammensee S, Leight JL, Georges PC, MacKintosh FC (2007) Negative normal stress in semiflexible biopolymer gels. Nat Mater 6: 48–51

    Article  Google Scholar 

  5. Storm C, Pastore JJ, Mackintosh FC, Lubensky TC, Janmey PA (2005) Nonlinear elasticity in biological gels. Nature 435: 191–194

    Article  Google Scholar 

  6. Pullarkat PA, Fernandez PA, Ott A (2007) Rheological properties of the Eukaryotic cell cytoskeleton. Phys Rep 449: 29–53

    Article  Google Scholar 

  7. Cox HL (1952) The elasticity and strength of paper and other fibrous materials. Br J Appl Phys 3: 72–79

    Article  Google Scholar 

  8. Wu XF, Dzenis YA (2005) Elasticity of planar fiber networks. J Appl Phys 98: 093501

    Article  Google Scholar 

  9. Wagner B, Tharmann R, Haase I, Fischer M, Bausch AR (2006) Cytoskeletal polymer networks: the molecular structure of cross-linkers determines macroscopic properties. Proc Natl Acad Sci USA 103: 13974–13978

    Article  Google Scholar 

  10. Gardel ML et al (2004) Elastic behavior of cross-linked and bundled actin networks. Science 304: 1301–1305

    Article  Google Scholar 

  11. Astrom JA, Timonen J, Myllys M, Fellman J, LeBell J (2007) Random networks of fibres display maximal heterogeneity in the distribution of elastic energy. Eur Phys J E 22: 61–66

    Article  Google Scholar 

  12. Astrom JA, Makinen JP, Alava MJ, Timonen J (2005) Elasticity of Poissonian fiber networks. Phys Rev E 61: 5550–5556

    Article  Google Scholar 

  13. Head DA, Levine AJ, MacKintosh FC (2003) Deformation of cross-linked semiflexible polymer networks. Phys Rev Lett 91: 108102

    Article  Google Scholar 

  14. Heussinger C, Frey E (2006) Stiff polymers, foams, and fiber networks. Phys Rev Lett 96: 017802

    Article  Google Scholar 

  15. Jaeger HM, Nagel SR, Behringer RP (1996) Granular solids, liquids, and gases. Rev Mod Phys 68: 1259–1273

    Article  Google Scholar 

  16. Tanguy A, Wittmer JP, Leonforte F, Barrat JL (2002) Continuum limit of amorphous elastic bodies: a finite-size study of low-frequency harmonic vibrations. Phys Rev B 66: 174205

    Article  Google Scholar 

  17. Leonforte F, Tanguy A, Wittmer JP, Barrat JL (2004) Continuum limit of amorphous elastic bodies. II. Linear response to a point source force. Phys Rev B 70: 014203

    Article  Google Scholar 

  18. Hatami-Marbini H, Picu RC (2009) An eigenstrain formulation for the prediction of elastic moduli of defective fiber networks. Eur J Mech A/Solids 28: 305–316

    Article  MATH  MathSciNet  Google Scholar 

  19. Wilhelm J, Frey E (2003) Elasticity of stiff polymer networks. Phys Rev Lett 91: 108103

    Article  Google Scholar 

  20. Liu J, Koenderink GH, Kasza KE, MacKintosh FC, Weitz DA (2007) Visualizing the strain field in semiflexible polymer networks: strain fluctuations and nonlinear rheology of F-actin gels. Phys Rev Lett 98: 198304

    Article  Google Scholar 

  21. Heussinger C, Schaefer B, Frey E (2007) Nonaffine rubber elasticity for stiff polymer networks. Phys Rev E 76: 031906

    Article  Google Scholar 

  22. Hatami-Marbini H, Picu RC (2008) Scaling of nonaffine deformation in random semiflexible fiber networks. Phys Rev E 77: 062103

    Article  Google Scholar 

  23. Hatami-Marbini H, Picu RC (2009) Effect of fiber orientation on the non-affine deformation of random fiber networks. Acta Mech 205: 77–84

    Article  MATH  Google Scholar 

  24. Kallmes O, Corte H (1960) The structure of paper. I. The statistical geometry of an ideal two dimensional fiber network. Tappi J 43: 737–752

    Google Scholar 

  25. Hatami-Marbini H, Picu RC (2009) Two-dimensional continuum map of filamentous random networks. Bioengineering Conference, IEEE 35th Annual Northeast, Boston, pp 1–2

  26. Falconer KJ (1990) Fractal geometry: mathematical foundations and applications. Wiley, New York

    MATH  Google Scholar 

  27. Head DA, Levine AJ, MacKintosh FC (2003) Distinct regimes of elastic response and deformation modes of cross-linked cytoskeletal and semiflexible polymer networks. Phys Rev E 68: 061907

    Article  Google Scholar 

  28. Kahle A, Winkler B, Radulescu A, Schreuer J (2004) Small-angle neutron scattering study of volcanic rocks. Eur J Miner 16: 407–417

    Article  Google Scholar 

  29. Majumdar S et al (1999) Fractal analysis of radiographs: assessment of trabecular bone structure and prediction of elastic modulus and strength. Med Phys 26: 1330–1340

    Article  Google Scholar 

  30. Parkinson IH, Fazzalari NL (2000) Methodological principles for fractal analysis of trabecular bone. J Microsc 198: 134–142

    Article  Google Scholar 

  31. Ma HS, Roberts AP, Prevost JH, Jullien R, Scherer GW (2000) Mechanical structure–property relationship of aerogels. J Non-Crystal Sol 277: 127–141

    Article  Google Scholar 

  32. Marliere C, Despetis F, Etienne P, Woignier T, Dieudonne P, Phalippou J (2001) Very large-scale structures in sintered silica aerogels as evidenced by atomic force microscopy and ultra-small angle X-ray scattering experiments. J Non-Crystal Sol 285: 148–153

    Article  Google Scholar 

  33. Maksym GN, Bates JHT (1997) A distributed nonlinear model of lung tissue elasticity. J Appl Physiol 82: 32–41

    Google Scholar 

  34. Vrieling EG et al (2004) Ultrasmall, small, and wide angle X-ray scattering analysis of diatom biosilica: interspecific differences in fractal properties. J Mater Chem 14: 1970–1975

    Article  Google Scholar 

  35. Nemat-Nasser S, Hori M (1993) Micromechanics: overall properties of heterogeneous materials. North-Holland, Amsterdam

    MATH  Google Scholar 

  36. Soare MA, Picu RC (2008) Boundary value problems defined on stochastic self-similar multiscale geometries. Int J Num Methods Eng 74: 668–696

    Article  MATH  MathSciNet  Google Scholar 

  37. Soare MA, Picu RC (2008) Spectral decomposition of random fields defined over the generalized cantor set. Chaos Solitons Fractals 37: 566–573

    Article  MATH  MathSciNet  Google Scholar 

  38. Kaye BH (1989) A random walk through fractal dimensions. VCH Publishers, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    R. C. Picu

  2. Mechanical Engineering Department, Stanford University, Stanford, CA, 94305, USA

    H. Hatami-Marbini

Authors
  1. R. C. Picu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Hatami-Marbini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. Hatami-Marbini.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Picu, R.C., Hatami-Marbini, H. Long-range correlations of elastic fields in semi-flexible fiber networks. Comput Mech 46, 635–640 (2010). https://doi.org/10.1007/s00466-010-0500-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-010-0500-6

Keywords

Search

Navigation