A random theory of deformation and flow of crystalline media, which is based upon statistical mechanics and the theory of probability, has been proposed in previous publications (1–3). Furthermore, for the viscoelastic relaxation of structured systems, a linear stochastic model approach, based upon this deformation theory, has been developed by introducing the Green’s impulse transfer function of system theory (4). All these dynamic models, however, only consider interaction effects in a very general form. It is the purpose of this paper to formulate interaction effects between constituents of a crystalline media in a more detailed manner and to present an analysis incorporating time-dependent surface effects.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    Axelrad, D. R., Stochastic Analysis of the Flow of Two-Phase Media. Proc. 5th Int. Cong, on Rheology 2, 221–231 (Tokyo 1970).Google Scholar
  2. 2).
    Axelrad, D. R., Arch. Mech. Stosowanej 23, 131 to 140 (1971).Google Scholar
  3. 3).
    Axelrad, D. R. and R. N. Yong, Micro-Rheology of the Yielding of a Heterogeneous Medium. Proc. 5th Int. Cong, on Rheology 2, 309–314 (1971).Google Scholar
  4. 4).
    Axelrad, D. R. and J. W. Provan, Rheol. Acta 10, 330–335 (1971).CrossRefGoogle Scholar
  5. 5).
    Provan, J. W., Arch. Mech. Stosowanej 23, 339 to 352 (1971).MathSciNetGoogle Scholar
  6. 6).
    Goux, C. et al., Theoretical and Experimental Determinations of Grain Boundary Structures and Energies. In: Grain Boundaries and Interfaces, Eds. P. Chaudhari and J. W. Matthews, North-Holland (1972).Google Scholar
  7. 7).
    Bollmann, W., Crystal Defects and Crystalline Interfaces (Berlin-Heidelberg-New York 1970).Google Scholar
  8. 8).
    Axelrad, D. R., D. Atack, and J. W. Provan, Rheol. Acta 12, 000–000 (1973).Google Scholar
  9. 9).
    Ziegler, H., Some Extremum Principles in Irreversible Thermodynamics with Application to Continuum Mechanics. In: Progress in Solid Mechanics 4, eds.: I. N. Sneddon and R. Hill (Amsterdam 1963).Google Scholar
  10. 10).
    Yvon, J., Correlations and Entropy in Classical Statistical Mechanics (London 1969).Google Scholar
  11. 11).
    Gel’Fand, I. M. and N. Ya. Vilenkin, Generalized Functions Vol. 4 (London-New York 1964).Google Scholar
  12. 12).
    Yaglom, A. M., An Introduction to the Theory of Stationary Random Functions (1962).Google Scholar
  13. 13).
    Axelrad, D. R. and J. Kalousek, Measurement of Microdeformations by Holographic X-Ray Diffraction. Paper 15, Int. Sym. on Experimental Mechanics, Univ. of Waterloo, Ontario, Canada, June 12-16, 1972.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • D. R. Axelrad
    • 1
  • J. W. Provan
    • 1
  1. 1.Micromechanics Lab.McGill UniversityMontrealCanada

Personalised recommendations