Abstract

In this work we extend the well-posedness for infinitesimal dislocation-based gradient viscoplasticity with linear kinematic hardening from the subdifferential case to general nonassociative monotone plastic flows. We assume an additive split of the displacement gradient into nonsymmetric elastic distortion and nonsymmetric 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 only of monotone type. Based on the generalized version of Korn’s inequality for incompatible tensor fields (the nonsymmetric plastic distortion) due to Neff et al. the existence of solutions of quasistatic initial-boundary value problems under consideration is shown using a time-discretization technique and a monotone operator method.

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