Journal of Applied Mechanics and Technical Physics

, Volume 59, Issue 6, pp 1078–1084 | Cite as

Entropy Interpretation of the Elastic–Plastic Strain Invariant

  • L. B. Zuev
  • A. G. Lunev
  • O. S. Staskevich


An interpretation of the nature of the relation between elastic and plastic strains, called the elastic–plastic strain invariant, is proposed which takes into account the change in the entropy of the system during autowave generation at the stage of linear strain hardening. It is shown that this approach consistently explains the nature of the invariant and its role in the description of plasticity.


plasticity elastic deformation plastic deformation localization elastic waves defects dislocations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. B. Zuev, V. I. Danilov, and S. A. Barannikova, Physics of Macrolocalization of Plastic Flow (Nauka, Novosibirsk, 2008) [in Russian].Google Scholar
  2. 2.
    V. I. Nekorkin and V. B. Kazantsev, “Autowaves and Solitons in a Three-Component Reaction-Diffusion System,” Int. J. Bifurcat. Chaos 12 (11), 2421–2434 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    V. A. Davydov, N. V. Davydov, V. G. Morozov, et al., “Autowaves in the Moving Excitable Media,” Condensed. Matter Phys. 7 (3), 565–578 (2004).CrossRefGoogle Scholar
  4. 4.
    S. A. Barannikova, M. V. Nadezhkin, and L. B. Zuev, “Relationship between Burgers Vectors of Dislocations and Plastic Strain Localization Patterns in Compression-Strained Alkali Halide Crystals,” Pis’ma Zh. Tekh. Fiz. 37 (16), 15–21 (2011).Google Scholar
  5. 5.
    L. B. Zuev, S. A. Barannikova, M. V. Nadezhkin, and V. V. Gorbatenko, “Localization of Deformation and Prognostibility of Rock Failure,” Fiz.-Tekh. Probl. Razrab. Polezn. Izkop., No. 1, 49–56 (2014).Google Scholar
  6. 6.
    K. Otsuka, K. Shimizu, “Pseudoelasticity and Shape Effects in Alloys,” Int. Metals Rev. 31 (3), 93–114 (1986).Google Scholar
  7. 7.
    V. F. Kurilov, L. B. Zuev, V. E. Gromov, et al., “Dynamic Deceleration of Dislocations in NaCl Crystals of Different Purity,” Kristallografiya 22 (3), 653–654 (1977).Google Scholar
  8. 8.
    E. V. Darinskaya, A. A. Urusovskaya, V. F. Opekunov, et al., “Study of Viscous Deceleration of Dislocations in LiF Crystals Based on the Mobility of Individual Dislocations,” Fiz. Tverd. Tela 20 (4), 1250–1252 (1978).Google Scholar
  9. 9.
    E. V. Darinskaya and A. A. Urusovskaya, “Viscous Deceleration of Dislocations in CsI Crystals at a Temperature of 77–300 K,” Fiz. Tverd. Tela 17 (8), 2421–2422 (1975).Google Scholar
  10. 10.
    L. B. Zuev, V. E. Gromov, and O. I. Aleksankina, “Dependence of Dislocation Velocity on Electric Field Intensity,” Kristallografiya 19 (4), 889–891 (1974).Google Scholar
  11. 11.
    L. B. Zuev, V. E. Gromov, V. F. Kurilov, and L. I. Gurevich, “Mobility of Dislocations in Zinc Single Crystals under the Action of Current Pulses,” Dokl. Akad. Nauk SSSR 239 (1), 874–876 (1978).Google Scholar
  12. 12.
    T. Suzuki, H. Yoshinaga, and S. Takeuchi, Dislocation Dynamics and Plasticity (Syokabo, Tokyo, 1986).Google Scholar
  13. 13.
    D. Hudson, Statistics (Geneva, 1964).Google Scholar
  14. 14.
    L. B. Zuev, “Elastic–Plastic Invariant Relation for Deformation of Solids,” Prikl. Mekh. Tekh. Fiz. 54 (1), 125–133 (2013) [J. Appl. Mech. Tech. Phys. 54 (1), 108–115 (2013)].Google Scholar
  15. 15.
    A. Seeger and W. Frank, “Structure Formation by Dissipative Processes in Crystals with High Defect Densities,” in Non-Linear Phenomena in Material Science (Trans. Tech. Publ., New York, 1987), pp. 125–138.Google Scholar
  16. 16.
    J. S. Langer, E. Bouchbinder, and T. Lookman, “Thermodynamic Theory of Dislocation-Mediated Plasticity,” Acta Mater. 58 (10), 3718–3732 (2010).CrossRefGoogle Scholar
  17. 17.
    A. Ishii, Yu Li, and S. Ogata, “Shuffling-Controlled versus Strain-Controlled Deformation Twinning: The Case for HCP Mg Twin Nucleation,” Int. J. Plasticity 82 (1), 32–43 (2016).CrossRefGoogle Scholar
  18. 18.
    Yu. L. Klimontovich, Introduction to the Physics of Open Systems (Yanus-K, Moscow, 2002) [in Russian].Google Scholar
  19. 19.
    L. B. Zuev, “Entropy of Waves of Localized Plastic Deformation,” Pis’ma Zh. Tekh. Fiz. 31 (3), 1–4 (2005).Google Scholar
  20. 20.
    J. F. Nye, Physical Properties of Crystals (Clarendon, Oxford, 1957).zbMATHGoogle Scholar
  21. 21.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 5: Statistical Physics (Nauka, Moscow, 1987; Pergamon Press, 1980).Google Scholar
  22. 22.
    Yu. B. Rumer and M. Sh. Ryvkin, Thermodynamics and Statistical Physics (Novosibirsk State University, Novosibirsk, 2000) [in Russian].Google Scholar
  23. 23.
    L. B. Zuev, “Macroscopic Physics of Plastic Deformation of Metals,” Usp. Fiz. Metal. 16 (1), 35–60 (2015).CrossRefGoogle Scholar
  24. 24.
    V. L. Gilyarov and A. I. Slutsker, “Energy Analysis of a Loaded Quantum Anharmonic Oscillator in a Wide Temperature Range,” Zh. Tekh. Fiz. 80 (5), 94–99 (2010).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Institute of Strength Physics and Materials Science, Siberian BranchRussian Academy of SciencesTomskRussia

Personalised recommendations