Skip to main content
Log in

On a certain idea of elastic and plastic strains of originally orthotropic body

  • Geomechanic
  • Published:
Journal of Mining Science Aims and scope

Abstract

A decomposition of the generalized Hooke's law for an initially orthotropic body into three plane-deformed states is considered. Under the assumption that the elastoplastic process is continuous, possible techniques for construction of the defining relations of plasticity which, in the limiting case of an initially orthotropic body, become well-known relations, are stated. It is established that, in the limiting situation, the schema of decomposition admits the existence of two moduli of elastic shear in the same direction. For this reason the schema, together with previously obtained plasticity relations, appears to be of doubtful validity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Haar and Th. Karman, “Zur Theorie der Spannungszustände in plastischen und sandartigen Medien,”Nachr. Königl. Gesellsch. Wissensch. Göttingen. Math.-Phys. KL, 1908.

  2. S. A. Khristianovich, “Deformation of a reinforced plastic body,”Mekh. Tverd. Tela, No. 2 (1974).

  3. Ye. I. Shemyakin, “Anisotropy of the plastic state,”Chisl. Met. Mekh. Sploshn. Sredy 4, No. 4 (1973).

  4. A. M. Kovrizhnykh, “Variant of theory of plastic deformation of rock,”Fiz.-Tekh. Probl. Raz. Polez. Iskop., No. 1 (1983).

  5. N. I. Muskhelishvili,Certain Fundamental Problems of the Mathematical Theory of Elasticity [in Russian], Akad. Nauk SSSR, Moscow (1949).

    Google Scholar 

  6. Ya. K. Rykhlevsky, “On Hooke's law,”Prikl. Mat. Mekh.,48, vyp. 3 (1984).

  7. A. I. Chanyshev, “On plasticity of anisotropic media,”Prikl. Mat. Tekh. Fiz., No. 2 (1984).

  8. S. G. Lekhnitsky,Theory of Elasticity of Anisotropic Bodies [in Russian], Gostekhizdat, Moscow (1950).

    Google Scholar 

  9. A. M. Kovrizhnykh, “Plastic deformation of reinforced materials in complex loading,”Mekh. Tverd. Tela, No. 4 (1986).

Download references

Authors

Additional information

Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 29–35, May–June, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chanyshev, A.I. On a certain idea of elastic and plastic strains of originally orthotropic body. J Min Sci 36, 220–226 (2000). https://doi.org/10.1007/BF02562523

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02562523

Keywords

Navigation