Geometry Method for Localization Analysis in Gradient-Dependent J2 Plasticity

Abstract

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.