A novel continuum approach to gradient plasticity based on the complementing concepts of dislocation and disequilibrium densities
Steinmann P, Kergaßner A, Landkammer P, Zbib HM (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Book Volume: 132
Article Number: 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.
Authors with CRIS profile
Paul Steinmann
Lehrstuhl für Technische Mechanik
Andreas Kergaßner
Lehrstuhl für Technische Mechanik
Philipp Landkammer
Lehrstuhl für Technische Mechanik
Involved external institutions
United States (USA) (US)How to cite
APA:
Steinmann, P., Kergaßner, A., Landkammer, P., & 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. https://dx.doi.org/10.1016/j.jmps.2019.103680
MLA:
Steinmann, Paul, et al. "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 (2019).
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