Non-associated plastic deformation and genuine instability

  • D. C. Drucker
  • M. Li
Part of the Acta Mechanica book series (ACTA MECH.SUPP., volume 3)


A non-associated flow rule often is employed to model the time-independent (elastic-plastic) behavior of materials sensitive to normal stress on planes of shear. To match the more moderate volume expansion observed, the plastic strain increment is taken as not normal to the current Mohr-Coulomb or similar yield surface. Unless the incremental elastic response were to override the plastic, however, there would be a genuine but limited instability of configuration for any such model subjected to a triaxial compression test. In fact, for the usual simple models, every state of stress in the plastic domain is unstable. The instability exhibited here is in the form of a rotating shear band. It is an initially accelerating instability, of limited total excursion, satisfying kinematics and kinetics. This instability of configuration would occur much earlier and differs fundamentally from the instability of the path of deformation customarily determined from the bifurcation condition for shear band formation under homogeneous stress and stress rate.


Shear Band Principal Stress Yield Surface Triaxial Test Stress Path 
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Copyright information

© Springer-Verlag Wien 1992

Authors and Affiliations

  • D. C. Drucker
    • 1
  • M. Li
    • 2
  1. 1.Department of Aerospace Engineering, Mechanics and Engineering ScienceUniversity of FloridaGainesvilleUSA
  2. 2.GainesvilleUSA

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