Well-posedness for dislocation based gradient visco-plasticity with isotropic hardening

In this work we establish the well-posedness for infinitesimal dislocation based gradient viscoplasticity with isotropic hardening for general subdifferential plastic flows. We assume an additive split of the displacement gradient into non-symmetric elastic distortion and non-symmetric plastic distortion. The thermodynamic potential is augmented with a term taking the dislocation density tensor Curlp into account. The constitutive equations in the models we study are assumed to be of self-controlling type. Based on the self-controlling property the existence of solutions of quasi-static initial–boundary value problems under consideration is shown using a time-discretization technique and a monotone operator method.