In this work the geometrical method for the assessment of discontinuous bifurcation conditions is extended to encompass gradient-dependent plasticity. To this end, the gradient-dependent localization condition is cast in the form of an elliptical envelope condition in the coordinates of Mohr. The results in this work demonstrate the capability of thermodynamically consistent gradient-dependent elastoplastic model formulations to suppress the localized failure modes of the classical plasticity that take place when the hardening/softening modulus H¯ equals the critical value for localization H¯c⁠, provided the characteristic length l remains positive.

Issue Section:
Technical Papers
Keywords:
elastoplasticity, bifurcation, hardening, softening, free energy
Topics:
Bifurcation, Elastoplasticity, Hardening, Plasticity, Constitutive equations, Failure mechanisms, Geometry, Stress, Failure
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