Vol. 1, No. 2, 2013

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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

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.

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
Received: 30 April 2012
Revised: 5 September 2012
Accepted: 20 October 2012
Published: 16 April 2013

Communicated by Francesco dell'Isola
Sergiy Nesenenko
Fachbereich Mathematik
Technische Universität Darmstadt
Schlossgartenstrasse 7
D-64289 Darmstadt
Patrizio Neff
Fakultät für Mathematik
Universität Duisburg-Essen
Campus Essen
Universitätsstrasse 2
D-45141 Essen