Skip to main content
SpringerLink
Log in

Self-diffusion in remodeling and growth

  • Published:
Zeitschrift für angewandte Mathematik und Physik Aims and scope Submit manuscript

Abstract

Self-diffusion, or the flux of mass of a single species within itself, is viewed as an independent phenomenon amenable to treatment by the introduction of an auxiliary field of diffusion velocities. The theory is shown to be heuristically derivable as a limiting case of that of an ordinary binary mixture.

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. Bowen R.M.: Theory of mixtures. In: Eringen, A.C. (ed.) Continuum Physics, vol. 3, pp. 2–127. Academic Press, London (1976)

    Google Scholar 

  2. Cowin S.C., Hegedus D.H.: Bone remodeling I: theory of adaptive elasticity. J. Elasticity 6, 313–326 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  3. Epstein M., Maugin G.A.: Thermomechanics of volumetric growth in uniform bodies. Int. J. Plasticity 16, 951–978 (2000)

    Article  MATH  Google Scholar 

  4. Epstein M., Elżanowski M.: Material Inhomogeneities and their Evolution. Springer, Berlin (2007)

    MATH  Google Scholar 

  5. Garikipati K., Arruda E.M., Grosh K., Narayanan H., Calve S.: A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics. J. Mech. Phys. Solids 52, 1595–1625 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kuhl E., Steinmann P.: Mass- and volume-specific views on thermodynamics for open systems. Proc. R. Soc. Lond. A459, 2547–2568 (2003)

    MathSciNet  Google Scholar 

  7. Truesdell, C.: Sulle basi della Termomeccanica. Rendiconti della Accademia Nazionale dei Lincei 22, 33–38, 158–166 (1957)

  8. Truesdell, C., Toupin, R.: The classical field theories. In: Flügge, S. Handbuch der Physik, vol. III/3, Springer, Berlin (1960)

Download references

Author information

Authors and Affiliations

  1. University of Calgary, Calgary, Canada

    Marcelo Epstein

  2. Oxford Centre for Collaborative Applied Mathematics, University of Oxford, Oxford, UK

    Alain Goriely

Authors
  1. Marcelo Epstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alain Goriely
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcelo Epstein.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Epstein, M., Goriely, A. Self-diffusion in remodeling and growth. Z. Angew. Math. Phys. 63, 339–355 (2012). https://doi.org/10.1007/s00033-011-0150-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00033-011-0150-3

Mathematics Subject Classification (2000)

Keywords

Search

Navigation