Views on multiplicative elastoplasticity and the continuum theory of dislocations

The objective of this contribution is a geometrically non-linear formulation of the continuum theory of dislocations within the framework of multiplicative elastoplasticity at finite strains. Thereby, the continuum theory of dislocations is particularly motivated by the kinematic structure of single crystals. Two different views on the continuum theory of dislocations at finite inelastic strains are adopted. Firstly, different dislocation density tensors are introduced from the viewpoint of continuum mechanics as the incompatibility of the so-called plastic intermediate configuration. Secondly, the continuum theory of dislocations is motivated as a Cartan differential geometry where the corresponding torsion tensor is associated to the dislocation density. Finally, as the main outcome of this contribution, the kinematically necessary dislocation density is considered within the exploitation of the thermodynamical principle of positive dissipation. As a result, a phenomenological description of hardening is obtained, which on the one hand incorporates second spatial derivatives of the plastic deformation gradient into the yield condition and on the other hand mimics the characteristic structure of kinematic hardening