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Materials Science

, Volume 43, Issue 2, pp 145–152 | Cite as

Comparative analysis of the theories of sliding with regular and singular loaded surfaces

  • M. Yu. Shvaiko
  • M. M. Fil’kevych
  • S. Yu. Estrin
Article
  • 19 Downloads

Abstract

We study the possibility of application of the versions of the theory of sliding [1] with regular and singular loading surfaces (Σ) under complex loads in the form of two-link paths and establish the relationships between the stress \((\dot \sigma _{ij} )\) and strain rates \((\dot \varepsilon _{ij} )\) in a small neighborhood of an angular point in the loading path. The advantages of the theory of sliding with singular surfaces are discussed and the impossibility of application of the theories of plastic flow with regular surfaces to the solution of the problems of stability of structural elements is demonstrated. However, their application to the solution of boundary-value problems of determination of the total strains can be reasonable.

Keywords

Plastic Flow Small Neighborhood Loading Path Stress Space Complex Loading 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    N. Yu. Shvaiko, “On the theory of plasticity based on the concept of sliding,” Prikl. Mekh., 12, No. 11, 12–24 (1976).Google Scholar
  2. 2.
    M. Yu. Shvaiko, “Concept of sliding and smooth loading surfaces in the theory of plasticity,” Dokl. Akad Nauk Ukr. SSR, Ser. A., No. 10, 58–63 (1980).Google Scholar
  3. 3.
    M. Yu. Shvaiko, “On the theory of plasticity with smooth loading surfaces,” Fiz.-Khim. Mekh. Mater., 33, No. 6, 63–73 (1997).Google Scholar
  4. 4.
    A. M. Zhukov, “Complex loading and the theories of plasticity of isotropic materials,” Izv. Akad. Nauk SSSR. Otd. Tekh. Nauk, No. 8, 81–92 (1955).Google Scholar
  5. 5.
    M. Ya. Leonov and B. A. Rychkov, “Development of the concept of sliding in the theory of plasticity,” Fiz.-Khim. Mekh. Mater., 18, No. 4, 3–12 (1982).Google Scholar
  6. 6.
    V. A. Sveshnikova, “On the plastic deformation of hardening metals,” Izv. Akad. Nauk SSSR. Otd. Tekh. Nauk, No. 1, 155–161 (1956).Google Scholar
  7. 7.
    Yu. I. Kadashevich and V. V. Novozhilov, “Theory of plasticity with regard for microstresses,” Prikl. Mekh. Mat., 22, No. 1, 78–89 (1958).Google Scholar
  8. 8.
    A. A. Il’yushin, Plasticity [in Russian], Izd. Akad. Nauk SSSR, Moscow (1963).Google Scholar
  9. 9.
    M. Yu. Shvaiko and M. M. Fil’kevych, “Analytic and experimental investigation of the deformation of 45 steel under complex loading,” Matem. Met. Fiz.-Mekh. Polya., 49, No. 1, 186–196 (2006).Google Scholar
  10. 10.
    É. I. Grigolyuk, “Theoretical and experimental investigation of the stability of thin shells beyond the limits of elasticity,” in: Itogi VINITI. Mechanics. Elasticity and Plasticity [in Russian], Moscow (1966), pp. 7–80.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • M. Yu. Shvaiko
    • 1
  • M. M. Fil’kevych
    • 1
  • S. Yu. Estrin
    • 1
  1. 1.Dnipropetrovs’k National UniversityDnipropetrovs’k

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