Well-posedness for dislocation based gradient visco-plasticity II: monotone case

In this work we continue to investigate the well-posedness for infinitesimal dislocation based gradient viscoplasticity with linear kinematic hardening. 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 into account. The constitutive equations in the models we study are assumed to be only of monotone type. Based on the generalized version of Korn’s inequality for incompatible tensor fields (the non-symmetric plastic distortion) due to Neff/Pauly/Witsch the existence of solutions of quasistatic initial-boundary value problems under consideration is shown using a time-discretization technique and a monotone operator method.