Skip to main content
SpringerLink
Log in

Mathematical description of surface effects in deformable solid bodies

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

We consider the general balance equations for the interface surface of two media and the interface line of three media, and we analyze the generalized Laplace and Young equations and study the “balance” equations for surface dislocations and disclinations. We establish the relations between the densities and flows of surface defects at the junction of three grain boundaries.

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

Literature cited

  1. V. P. Alekhin,The Physics of Durability and Plasticity of Surface Layers of Materials [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  2. P. A. Bereznyak, V. S. Boiko, and I. M. Mikhailovskii, “A new type of defect having the structure of large-angle grain boundaries. Radiationally stimulated grain boundary slippage,”Vopr. Atom. Nauki i Tekh., Fiz. Rad. Povr. Rad. Materialoved., No. 1, 19–23 (1988).

    Google Scholar 

  3. A. M. Kosevich and Yu. A. Kosevich, “A step on the surface of a crystal formed by the emergence of a boundary dislocation,”Fiz. Nizk. Temp.,7, No. 10, 1347–1349.

  4. M. A. Krishtal, A. A. Borgardt, and P. V. Loshkarev, “Acoustic emission under interaction of iron and its alloys with surface-active melts,”Dokl. Akad. Nauk SSSR,267, No. 3, 626–629 (1982).

    Google Scholar 

  5. M. A. Krishtal, P. V. Loshkarev, and A. A. Borgardt, “On the conditions for appearance of an embryo crack under liquid-metal brittleness,” in:The Mechanisms of Dynamic Deformations of Materials [in Russian], Kuibyshev Politekh. Inst. (1986), pp. 131–134.

  6. Ya. S. Pidstrigach, “The differential equations of the problem of thermodiffusion in a solid deformable isotropic body,”Dop. Akad. Nauk Ukr. RSR, No. 2, 169–172 (1961).

    Google Scholar 

  7. Yu. Z. Povstenko, “The influence of inhomogeneity of the distribution of surface energy on the stressed state in an elastic half-space,”Mat. Met. i Fiz.-Mekh. Polya, No. 9, 84–87 (1979).

    Google Scholar 

  8. Yu. Z. Povstenko, “Conditions on the line of contact of three media,”Prikl. Mat. i Mekh.,45, No. 5, 919–923 (1981).

    Google Scholar 

  9. Yu. Z. Povstenko, “The continuous theory of dislocations and disclinations in a two-dimensional medium,”Prikl. Mat. i Mekh.,49, No. 6, 1026–1031 (1985).

    Google Scholar 

  10. Yu. Z. Povstenko, “Influence of the gradient of surface tension on the stresses in a solid body,”Fiz. Khim. Mekh. Mater., No. 3, 88–91 (1989).

    Google Scholar 

  11. Yu. Z. Povstenko, “On the limiting angle of wetting of inhomogeneous surfaces,”Dokl. Akad. Nauk. Ukr. SSR, Ser. A, No. 11, 46–48 (1989).

    Google Scholar 

  12. Yu. Z. Povstenko, “Anisotropy of wetting and spreading,”Mat. Met. i Fiz.-Mekh. Polya, No. 31, 8–16 (1990).

    Google Scholar 

  13. Ya. S. Podstrigach and Yu. Z. Povstenko,Introduction to the Mechanics of Surface Effects in Deformable Solid Bodies [in Russian], Naukova Dumka, Kiev (1985).

    Google Scholar 

  14. Ya. S. Podstrigach and P. R. Shevchuk, “A study of the stressed state of solid bodies with foreign inclusions and thin coatings under change in temperature,”Probl. Prochn., No. 11, 37–40 (1970).

    Google Scholar 

  15. A. B. D. Cassie, “Contact angles,”Disc. Faraday Soc, No. 3, 11–16 (1948).

    Google Scholar 

  16. R. Ghez, “A generalized Gibbsian surface,”Surface Sci.,4, No. 2, 125–140 (1966).

    Google Scholar 

  17. W. F. Harris, “The geometry of disclinations in crystals,” in:Surface and Defect Properties of Solids, Vol. 3, Burlington House, London (1974), pp. 57–92.

    Google Scholar 

  18. A. M. Kosevich and Yu. A. Kosevich, “Interaction of a dislocation with a crystal surface and emergence of dislocations onto a surface,” in:The Structure and Properties of Crystal Defects, Elsevier, Amsterdam (1984), pp. 397–405.

    Google Scholar 

  19. Yu. Z. Povstenko, “Analysis of motor fields in Cosserat continua of two and one dimensions and its applications,”Z. Angew. Math. Mech.,66, No. 10, 505–507 (1986).

    Google Scholar 

  20. Yu. Z. Povstenko, “Connection between non-metric differential geometry and mathematical theory of imperfections,”Int. J. Eng. Sci.,28, No. 12, 1321–1328 (1990).

    Google Scholar 

Download references

Authors
  1. Yu. Z. Povstenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 42–47.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Povstenko, Y.Z. Mathematical description of surface effects in deformable solid bodies. J Math Sci 67, 2852–2856 (1993). https://doi.org/10.1007/BF01095857

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01095857

Keywords

Search

Navigation