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In this work we establish the well-posedness for infinitesimal dislocationbased gradient viscoplasticity with isotropic hardening for general gradientmonotone plastic flows. We assume an additive split of the displacementgradient into non-symmetric elastic distortion and non-symmetric plasticdistortion. The thermodynamic potential is augmented with a term taking thedislocation density tensor $\operatorname{Curl} p$ into account. Theconstitutive equations in the models we study are assumed to be ofself-controlling type. Based on the generalized version of Korn's inequalityfor incompatible tensor fields (the non-symmetric plastic distortion) due toNeff/Pauly/Witsch the existence of solutions of quasi-static initial-boundaryvalue problems under consideration is shown using a time-discretizationtechnique and a monotone operator method.

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