On the formulation of higher gradient single and polycrystal plasticity

This contribution aims in a geometrically linear formulation of higher grad ient plasticity of single and polycrystalline material based on the continu um theory of dislocations and incompatibilities. Thereby, general continuum dislocation densities and incompatibilities are introduced from the viewpo int of continuum mechanics by considering the spatial closure failure of ar bitrary line integrals of the displacement differential. Then these finding s are translated to the plastic parts of the displacement gradient, the so called plastic distorsion, and the plastic strain, respectively, within an elasto-plastic solid thus defining tensor fields of plastic dislocation den sities and plastic incompatibilities. Next, in the case of single crystalli ne material the plastic dislocation density and in the case of polycrystall ine material the plastic incompatibility are considered within the exploita tion of the thermodynamical principle of positive dissipation. As a result, a phenomenological but physically motivated description of hardening is ob tained, which incorporates for single crystals second spatial derivatives o f the plastic deformation gradient and for polycrystals fourth spatial deri vatives of the plastic strains into the yield condition. Moreover, these mo difications mimic, the characteristic structure of kinematic hardening, whe reby the backstress obeys a nonlocal evolution law.