Existence results in dislocation based rate-independent isotropic gradient plasticity with kinematical hardening and plastic spin: The case with symmetric local backstress

2015/04/08 by Francois Ebobisse, Ebobisse, Francois, Patrizio Neff +3
Mathematics · #35B65 #35D10 #35J25 #74C10 #74D10 #75C05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B65 #msc:35D10 #msc:35J25 #msc:74C10 #msc:74D10 #msc:75C05

paper · pdf · doi:10.48550/arxiv.1504.01973

28 pages

arxiv created 2015/04/08 · arxiv updated 2015/04/09

Abstract

In this paper we use convex analysis and variational inequality methods to establish an existence result for a model of infinitesimal rate-independent gradient plasticity with kinematic hardening and plastic spin, in which the local backstress tensor remains symmetric. The model features a defect energy contribution which is quadratic in the dislocation density tensor Curl p, giving rise to nonlocal non-symmetric kinematic hardening. Use is made of a recently established Korn's type inequality for incompatible tensor fields. The solution space for the non-symmetric plastic distortion is naturally H(Curl) together with suitable tangential boundary conditions on the plastic distortion. Connections to other models are established as well.

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