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arXiv · 1411.1295

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

Nataliya Kraynyukova·Patrizio Neff·Sergiy Nesenenko·Krzysztof Chełmiński
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Abstract

In this work we establish the well-posedness for infinitesimal dislocation based gradient viscoplasticity with isotropic hardening for general gradient monotone plastic flows. 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 $\operatorname{Curl} p$ into account. The constitutive equations in the models we study are assumed to be of self-controlling 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 quasi-static initial-boundary value problems under consideration is shown using a time-discretization technique and a monotone operator method.

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Nataliya Kraynyukova, Patrizio Neff, Sergiy Nesenenko, Krzysztof Chełmiński. 2014-11-05. Well-posedness for dislocation based gradient visco-plasticity with isotropic hardening. https://arxiv.org/abs/1411.1295

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