Creep and Stress Relaxation in the Case of Loading and Unloading of a Cylindrical Layer with Allowance for the Development and Deceleration of a Viscoplastic Flow

  • A. S. Begun
  • L. V. KovtanyukEmail author
  • A. O. Lemza


The theory of large deformations is used to solve the problem of deformation of an elastoviscoplastic material placed in a gap between two coaxial cylindrical surfaces, with one of them rotating with an alternating rate and the other one at rest. It is shown that an increase in the stresses in a cylindrical layer due to a mechanical influence on it initially causes irreversible creep strains because of viscosity of the material and then the accumulation of plastic strains because of the arrival of stress states at the loading surface. The unloading is accompanied by a plastic strain and then a viscous one. The stress-strain parameters of the medium with a varying rotation rate of the cylinder are calculated. Stress relaxation after the complete stop of a cylinder is described.


elasticity plasticity creep viscosity large deformations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. I. Oleinikov and A. I. Pekash, Integrated Design of Manufacture of Monolithic Panels (Ekom, Moscow, 2009) [in Russian]Google Scholar
  2. 2.
    E. H. Lee, “Elastic-Plastic Deformation at Finite Strains,” Trans. ASME, J. Appl. Mech. 36, 1–6 (1969).ADSCrossRefzbMATHGoogle Scholar
  3. 3.
    V. I. Levitas, Large Elastoplastic Deformations of Materials under a High Pressure (Naukova Dumka, Kiev, 1987) [in Russian].Google Scholar
  4. 4.
    V. P. Myasnikov, “Motion Equations of Elastoplastic Materials under Large Deformations,” Vest. Dal’nevost. Otd. Ross. Akad. Nauk, No. 4, 8–13 (1996).Google Scholar
  5. 5.
    A. A. Burenin, G. I. Bykovtsev, and L. V. Kovtanyuk, “A Simple Model for an Elastoplastic Medium under Finite Deformations,” Dokl. Akad. Nauk 347 (2), 199–201 (1996).zbMATHGoogle Scholar
  6. 6.
    A. A. Burenin and L. V. Kovtanyuk, Large Irreversible Deformations and Elastic Aftereffect (Dal’nauka, Vladivostok, 2013) [in Russian].Google Scholar
  7. 7.
    S. V. Belykh, K. S. Bormotin, A. A. Burenin, et al., “Large Isothermal Deformations of Materials with Elastic, Viscous, and Plastic Properties,” Vestn. Chuvash. Gos. Ped. Univ. Yakovleva, Ser. Mekh. Pred. Sost., No. 4, 144–156 (2014).Google Scholar
  8. 8.
    A. S. Begun, A. A. Burenin, and L. V. Kovtanyuk, “Large Irreversible Deformations in the Case of Varying Mechanisms of Their Manufacture and the Problem of Specifying Plastic Potentials,” Dokl. Akad. Nauk 470 (3), 275–278 (2016).MathSciNetGoogle Scholar
  9. 9.
    A. S. Begun, L. V. Kovtanuyk, and A. O. Lemza, “Change of Mechanisms of Accumulation of Irreversible Deformations of Materials on an Example of Their Viscometric Deformation,” Izv. Ross. Akad. Nauk, Mekh. Tv. Tela, No. 1, 103–112 (2018).Google Scholar
  10. 10.
    A. A. Burenin, K. N. Galimzyanova, L. V. Kovtanyuk, and G. L. Panchenko, “Agreement of Growth Mechanisms of Irreversible Deformations of a Hollow Sphere under a Triaxial Compression,” Dokl. Akad. Nauk 482 (4), 403–406 (2018).Google Scholar
  11. 11.
    A. I. Lurie, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980; North Holland, 1990).Google Scholar
  12. 12.
    F. H. Norton, The Creep of Steel at High Temperatures (McGraw-Hill, New York, 1929).Google Scholar
  13. 13.
    A. S. Begun, A. A. Burenin, S. G. Zhilin, and L. V. Kovtanyuk, “Accounting for the Elastic Properties of Viscoplastic Lubricant Between Coaxial Rotating Cylinders,” Prikl. Mekh. Tekh. Fiz. 56 (3), 213–223 (2015) [J. Appl. Mech. Tech. Phys. 56 (3), 530–539 (2015)].zbMATHGoogle Scholar
  14. 14.
    A. S. Begun, A. A. Burenin, and L. V. Kovtanyuk, “Flow of an Elastoviscoplastic Material between Rotating Cylindrical Surfaces with Nonrigid Cohesion,” Prikl. Mekh. Tekh. Fiz. 56 (2), 146–158 (2015) [J. Appl. Mech. Tech. Phys. 56 (2), 293–303 (2015)].MathSciNetzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Automation and Control Processes, Far Eastern BranchRussian Academy of SciencesVladivostokRussia
  2. 2.Far Eastern Federal UniversityVladivostokRussia

Personalised recommendations