Deformation and Loss of Stability Modeling for Elastic-Viscoplastic Mixtures


To describe the behavior of a number of real structures consisting of n components, a generalized model of an elastic-viscoplastic body is used. Within the framework of the proposed model of a multicomponent body in a rigorous linearized three-dimensional formulation, the stability of multicomponent elastic-viscoplastic mixtures is investigated. It is shown that the study of the stability of the subcritical state of the mixture can be reduced to studying the stability of the continuum with complex physical and mechanical parameters. For homogeneous ground states, solutions of static linearized problems are given. An example is considered.

This is a preview of subscription content, access via your institution.


  1. 1

    A. N. Guz and A. N. Sporykhin, “Three-dimensional theory of inelastic stability (general questions),” Sov. Appl. Mech. 18, 581–597 (1982).

    ADS  MathSciNet  Article  Google Scholar 

  2. 2

    A. N. Guz and A. N. Sporykhin, “Three-dimensional theory of inelastic stability specific results,” Sov. Appl. Mech. 18, 671–693 (1982).

    ADS  Article  Google Scholar 

  3. 3

    A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies (Springer-Verlag, Berlin, 1999).

    Google Scholar 

  4. 4

    A. N. Sporykhin, Perturbation Method in Stability Problems for Complex Media (Voronezh. Gos. Univ., Voronezh, 1997) [in Russian].

    Google Scholar 

  5. 5

    A. N. Guz, Foundations of Stability Theory of Mine Workings (Naukova Dumka, Kiev, 1977) [in Russian].

    Google Scholar 

  6. 6

    A. N. Sporykhin and A. I. Shashkin, Stability of Equilibrium of Bulk Solids and Problems of Rock Mechanics (Fizmatlit, Moscow, 2004) [in Russian].

    Google Scholar 

  7. 7

    D. V. Gotsev and A. N. Sporykhin, Perturbation Method in Stability Problems of Supported Excavations (Voronezh. Gos. Univ., Voronezh, 2010) [in Russian].

    Google Scholar 

  8. 8

    A. N. Sporykhin, Non-Conservative Problems of Three-Dimensional Theory of Non-Elastic Stability in Geomechanics (Voronezh. Gos. Univ., Voronezh, 2015) [in Russian].

    Google Scholar 

  9. 9

    M. Reiner, Reology (Nauka, Moscow, 1965)[in Russian].

    Google Scholar 

  10. 10

    D. D. Ivlev and G. I. Bykovtsev, The Theory of a Hardening Plastic Body (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  11. 11

    A. N. Sporykhin, “Stability of deformation of viscoelasticplastic bodies,” J. Appl. Mech. Tech. Phys., No. 4, 34–38 (1967).

  12. 12

    A. N. Sporykhin, “A model for elastic-viscoplastic,” in Proc. of the IX All-Russian Conf. Mechanics of Solids, Voronezh, September 12–15, 2016 (Voronezh. Gos. Univ., Voronezh, 2019), pp. 199–201.

  13. 13

    A. I. Lur’e, “On the theory of the system of linear differential equations with the constant coefficients,” Tr. Leningr. Ind. Inst. 3 (6), 31–36 (1937).

    Google Scholar 

  14. 14

    M. A. Biot, Mechanics of Incremental Deformation (John Willey and Sons, New York, 1965).

    Google Scholar 

Download references

Author information



Corresponding author

Correspondence to A. N. Sporykhin.

Additional information

Translated by A. A. Borimova

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sporykhin, A.N. Deformation and Loss of Stability Modeling for Elastic-Viscoplastic Mixtures. Mech. Solids 55, 878–884 (2020).

Download citation


  • mixtures
  • stresses
  • deformations
  • plasticity
  • viscosity
  • stability