A novel continuum approach to gradient plasticity based on the complementing concepts of dislocation and disequilibrium densities

Steinmann, P. , Kergaßner, A., Landkammer, P. and Zbib, H. M. (2019) A novel continuum approach to gradient plasticity based on the complementing concepts of dislocation and disequilibrium densities. Journal of the Mechanics and Physics of Solids, 132, 103680. (doi: 10.1016/j.jmps.2019.103680)

Abstract

A geometrically linear continuum mechanics framework is proposed for gradient plasticity combining ’strain gradients’ and, with a novel approach, ’stress gradients’. Thereby the duality of kinematic and kinetic quantities is exploited in view of the ’div-grad-curl orthogonality’ in continuum field theories. On the one hand the non-integrability of the plastic distortion results in the well-established dislocation density - often denoted as the geometrically-necessary-dislocation (GND) density - that enters the energy storage function. On the other hand - as entirely novel concept introduced in this contribution - the non-equilibrium of the plastic stress results in the disequilibrium density that parameterizes the dual dissipation potential within the convex analysis setting of plasticity. Consequently both, the dislocation density as well as the disequilibrium density contribute in modelling the size-dependent hardening state of a material in a continuum mechanics setting. The novel approach is eventually elucidated in much detail for the specific case of single crystal plasticity.

• Item Type: Articles
• Additional Information: PS gratefully acknowledges support by the German Science Foundation through the project P10 of the Priority Programme 2013 on ’Residual Stresses’ and the project C5 of the Collaborative Research Centre 814 on ’Additive Manufacturing’ as well as by the Royal Society, UK, through a Wolfson Research Merit Award.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul
• Authors: Steinmann, P., Kergaßner, A., Landkammer, P., and Zbib, H. M.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Journal of the Mechanics and Physics of Solids
• Publisher: Elsevier
• ISSN: 0022-5096
• ISSN (Online): 0022-5096
• Published Online: 08 August 2019
• Copyright Holders: Copyright © 2019 Elsevier Ltd.
• First Published: First published in Journal of the Mechanics and Physics of Solids 132: 103680
• Publisher Policy: Reproduced in accordance with the publisher copyright policy