Development of a rectilinear axisymmetric viscoplastic flow and elastic aftereffect after its stop



An analytical solution is given for the boundary-value problem of the theory of large elastoviscoplastic strains for rectilinear motion of a material in the gap between two rigid coaxial cylindrical surfaces. The cases of initially uniformly accelerated motion with the subsequent uniformly decelerated stop of one of the surfaces when the other surface remains motionless are considered. The laws of motion of the elastoplastic boundaries and distributions of displacements and stresses, including residual ones, are given.

Key words

elasticity viscoplasticity large strains residual stress 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. P. Myasnikov, “Some exact solutions for rectilinear motions of viscoplastic media,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 54–60 (1961).Google Scholar
  2. 2.
    P. M. Ogibalov and A. Kh. Mirzadzhanzade, Nonstationary Motion of Viscoplastic Media [in Russian], Izd. Mosk. Univ., Moscow (1970).Google Scholar
  3. 3.
    G. I. Bykovtsev and A. D. Chernyshov, “On viscoplastic flow in noncircular cylinders with pressure drop,” Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 94–96 (1964).Google Scholar
  4. 4.
    A. A. Burenin, G. I. Bykovtsev, and L. V. Kovtanyuk, “One simple model for an elastoplastic medium for finite strains,” Dokl. Ross. Akad. Nauk, 347, No. 2, 199–201 (1996).Google Scholar
  5. 5.
    L. V. Kovtanyuk, “Modeling of large elastoplastic strains in the nonisothermal case,” Dal’nevost. Mat. Zh., 5, No. 1, 107–117 (2004).Google Scholar
  6. 6.
    L. V. Kovtanyuk and A. V. Shitikov, “On the theory of large elastoplastic strains taking into account temperature and rheological effects,” Vestn. Dal’nevost. Otd. Ross. Akad. Nauk, No. 4, 87–93 (2006).Google Scholar
  7. 7.
    V. P. Myasnikov, “The equations of motion of elastoplastic materials at large strains,” Vestn. Dal’nevost. Otd. Ross. Akad. Nauk, No. 4, 8–13 (1996).Google Scholar
  8. 8.
    V. A. Znamenskii and D. D. Ivlev, “On the equations of a viscoplastic body with piecewise linear potentials,” Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 6, 114–118 (1963).Google Scholar
  9. 9.
    G. I. Bykovtsev and T. D. Semykina, “On viscoplastic flow of round plates and shells of revolution,” Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 4, 68–76 (1964).Google Scholar

Copyright information

© MAIK/Nauka 2010

Authors and Affiliations

  • A. A. Burenin
    • 1
  • L. V. Kovtanyuk
    • 1
  • A. L. Mazelis
    • 1
  1. 1.Institute of Automatics and Control Processes, Far-East DivisionRussian Academy of SciencesVladivostokRussia

Personalised recommendations