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Crystals 2017, 7(8), 235; doi:10.3390/cryst7080235

On the Derivation of Boundary Conditions for Continuum Dislocation Dynamics

Institut für Festigkeitslehre, Technische Universität Graz, Kopernikusgasse 24, 8010 Graz, Austria
Received: 10 July 2017 / Revised: 27 July 2017 / Accepted: 28 July 2017 / Published: 30 July 2017
(This article belongs to the Special Issue Plasticity of Crystals and Interfaces)
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Abstract

Continuum dislocation dynamics (CDD) is a single crystal strain gradient plasticity theory based exclusively on the evolution of the dislocation state. Recently, we derived a constitutive theory for the average dislocation velocity in CDD in a phase field-type description for an infinite domain. In the current work, so-called rational thermodynamics is employed to obtain thermodynamically consistent boundary conditions for the dislocation density variables of CDD. We find that rational thermodynamics reproduces the bulk constitutive equations as obtained from irreversible thermodynamics. The boundary conditions we find display strong parallels to the microscopic traction conditions derived by Gurtin and Needleman (M.E. Gurtin and A. Needleman, J. Mech. Phys. Solids 53 (2005) 1–31) for strain gradient theories based on the Kröner–Nye tensor. View Full-Text
Keywords: continuum dislocation dynamics; strain gradient plasticity; boundary conditions; thermodynamic consistency; micro stresses; micro tractions continuum dislocation dynamics; strain gradient plasticity; boundary conditions; thermodynamic consistency; micro stresses; micro tractions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hochrainer, T. On the Derivation of Boundary Conditions for Continuum Dislocation Dynamics. Crystals 2017, 7, 235.

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