Strength of Materials

, Volume 32, Issue 1, pp 41–48 | Cite as

Exact solution of flow theory problems with isotropic-kinematic hardening. Part 2. Setting of the deformation trajectory in the spaces of total and plastic strains

  • V. A. Romashchenko
  • P. P. Lepikhin
  • K. B. Ivashchenko
Scientific and Technical Section


For an arbitrary isotropic and linear kinematic hardening and loading paths given in the form of arbitrary multisection polygonal lines in the five-dimensional deviatoric space of total strains, we have studied analytically an initially isotropic elastoplastic material with von Mises yielding and the associated flow rule. The solutions obtained are valid for arbitrary relationships that govern the variation of the spherical component of the stress tensor. For arbitrary isotropic and kinematic hardening, we have also obtained an analytical solution to an elastoplastic problem for an arbitrary deformation trajectory given in the deviatoria space of plastic strains


Plastic Strain Total Strain Yield Surface Kinematic Hardening Deformation Path 
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  1. 1.
    V. A. Romashchenko, P. P. Lepikhin, and K. B. Ivashchenko, “Exact solution of flow theory problems with isotropic-kinematic hardening. Part 1. Setting of the loading trajectory in the spaces of stresses,”Probl. Prochn., No. 6, 81–92 (1999).Google Scholar
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    Yu. I. Kadashevich and V. V. Novozhilov, “Plasticity theory accounting for residual microstresses,”Prikl. Matem. Mekh.,22, No. 1, 78–89 (1958).Google Scholar
  3. 3.
    P. P. Lepikhin, “Simulation of elastoplastic processes of deformation along trajectories in the form of two-section polygonal lines,”Probl. Prochn., No. 7, 7–12 (1980).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 2000

Authors and Affiliations

  • V. A. Romashchenko
  • P. P. Lepikhin
  • K. B. Ivashchenko

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