On the continuum formulation of higher gradient plasticity for single and polycrystals

This paper develops a geometrically linear formulation of higher gradient p lasticity of single and polycrystalline material based on the continuum the ory of dislocations and incompatibilities. As a result, a phenomenological but physically motivated description of hardening is obtained, which incorp orates for single crystals second order spatial derivatives of the plastic deformation gradient and for polycrystals fourth order spatial derivatives of the plastic strains into the yield condition. Moreover, these modificati ons mimic the characteristic structure of kinematic hardening, whereby the backstress obeys a nonlocal evolution law. For the one-dimensional example of an infinite shear layer the relation between the characteristic length I and the width w of a localized elasto-plastic shear band is examined in de tail for both cases. (C) 2000 Elsevier Science Ltd. All rights reserved.