Archive of Applied Mechanics

, Volume 88, Issue 12, pp 2221–2230 | Cite as

Strips of localization of plastic deformation

  • R. R. LabibovEmail author
  • Yu. A. Chernyakov
  • A. E. Sheveleva
  • A. G. Shevchenko


Model of slip band propagation in materials with yielding plateau is introduced. Development of a slip band is modeled in a form of loss of stability during transition of the material from an elastic state to hardening. This transition is the generalization of crack mode I development model by Novozhilov (J Appl Math Mech 3:201–210, 1969) in elastic solids. Possibility for slip bands of limited length is shown in the model in contrast to ideal plasticity model that only leads to infinite slip bands. Problems of localization in a form of slip bands in a state for the pure shear and for intermaterial layer are considered. For different external loads and various mechanical properties of the interlayer, the lengths of the localization zone of plastic deformations, the graphs of the tangential displacement jump in this zone, and the shear stress on their continuation are found.


Localization strip of plastic deformation Piecewise analytic function Shear displacement jumps 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • R. R. Labibov
    • 1
    Email author
  • Yu. A. Chernyakov
    • 1
  • A. E. Sheveleva
    • 2
  • A. G. Shevchenko
    • 1
  1. 1.Department of Theoretical and Computer MechanicsDnipro National UniversityDniproUkraine
  2. 2.Department of Computational Mathematics and Mathematical CyberneticsDnipro National UniversityDniproUkraine

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