Acta Mechanica

, Volume 92, Issue 1, pp 209–225

On the gradient-dependent theory of plasticity and shear banding

  • H. M. Zbib
  • E. C. Aifantis
Contributed Papers

DOI: 10.1007/BF01174177

Cite this article as:
Zbib, H.M. & Aifantis, E.C. Acta Mechanica (1992) 92: 209. doi:10.1007/BF01174177


After a brief review of a recently developed gradient-dependent theory of plasticity various questions related to the yield function and the loading-unloading condition in the presence of higher order strain gradients and the determination of the corresponding phenomenological coefficients are addressed. For rate-independent materials, we construct as before an analytical solution for the strain profile in the postlocalization regime providing the shear band thickness and strain within it but we now compare these results to recently obtained experimental data by assigning appropriate values to the gradient coefficients. We also address some questions recently raised in the literature regarding our nonlinear shear band analysis. For rate-dependent materials, the resulting spatio-temporal differential equation for the strain is solved numerically using the finite difference method. It is shown that the band width does not depend on the grid size, as long as the the grid size is smaller than a certain characteristic length. Various initial imperfections of different amplitudes and sizes are examined, and the possibility of simultaneous development of two shear bands and their interaction is investigated.

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • H. M. Zbib
    • 1
  • E. C. Aifantis
    • 2
  1. 1.Department of Mechanical and Materials EngineeringWashington State UniversityPullmanU.S.A.
  2. 2.Department of Mechanical Engineering and Engineering MechanicsMichigan Technological UniversityHoughtonU.S.A.