Well-posedness for dislocation based gradient visco-plasticity with isotropic hardening. (October 2015)

• Record Type: Journal Article
• Authors: Kraynyukova, N.; Nesenenko, S.; Neff, P.; Chełmiński, K.
• Is Part Of: Nonlinear analysis. Volume 25(2015)
• Page Start: 96
• Page End: 111
• Publication Date: 2015-10
• Subjects: Gradient viscoplasticity -- Rate dependent response -- Subdifferential flow rule -- Rothe's time-discretization method -- Maximal monotone method -- Geometrically necessary dislocations -- Plastic spin -- Defect energy; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2015.03.004
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this work we establish the well-posedness for infinitesimal dislocation based gradient viscoplasticity with isotropic hardening for general subdifferential 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 Curl p into account. The constitutive equations in the models we study are assumed to be of self-controlling type. Based on the self-controlling property 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.