#### Vol. 1, No. 2, 2013

 Recent Issues Volume 5, Issue 1 Volume 4, Issue 3+4 Volume 4, Issue 2 Volume 4, Issue 1 Volume 3, Issue 4 Volume 3, Issue 3 Volume 3, Issue 2 Volume 3, Issue 1 Volume 2, Issue 2 Volume 2, Issue 1 Volume 1, Issue 2 Volume 1, Issue 1
 The Journal Cover About the Journal Editorial Board Submission Guidelines Submission Form Ethics Statement Editorial Login Contacts ISSN: 2325-3444 (e-only) ISSN: 2326-7186 (print)
Well-posedness for dislocation-based gradient viscoplasticity, II: General nonassociative monotone plastic flows

### Sergiy Nesenenko and Patrizio Neff

Vol. 1 (2013), No. 2, 149–176
##### 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 $Curl\phantom{\rule{0.3em}{0ex}}p$ 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.

##### Keywords
plasticity, gradient plasticity, viscoplasticity, rate-dependent response, nonassociative flow rule, dislocations, plastic spin, Rothe's time-discretization method, maximal monotone method, Korn's inequality for incompatible tensor fields
##### Mathematical Subject Classification 2000
Primary: 35B65, 35D10, 74C10, 74D10
Secondary: 35J25, 34G20, 34G25, 47H04, 47H05