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

This paper develops a geometrically linear formulation of higher gradient plasticity of single and polycrystalline material based on the continuum theory of dislocations and incompatibilities. As a result, a phenomenological but physically motivated description of hardening is obtained, which incorporates 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 modifications 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 l and the width w of a localized elasto-plastic shear band is examined in detail for both cases