Geometry method for localization analysis in gradient-dependent [J.sub.2] plasticity

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 [bar.H] equals the critical value for localization [[bar.H].sub.c], provided the characteristic length l remains positive. [DOI: 10.1115/1.2202348]