Recent Developments in Gradient Plasticity—Part I: Formulation and Size Effects

Abstract

The purpose of this two-part article, is first to give an update of recent developments of gradient plasticity as this was advanced by Aifantis and co-workers in the early eighties to address dislocation patterning and shear band problems, and then to elaborate on two specific issues of current interest: size effects and plastic heterogeneity. In Part I, a brief review of gradient dislocation dynamics as providing a direct motivation for the simplest form of gradient plasticity is given. Then, a more general phenomenological formulation of gradient plasticity is given and used to interpret size effects. In Part II, wavelet analysis is used as a potential tool to describe plastic heterogeneity at very fine scales for which experimental results are not available, as well as for providing another means to interpret size effects through the derivation of scale-dependent constitutive equations.