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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012003449
pages 551-565

THEORETICAL AND ALGORITHMIC FORMULATION OF MODELS FOR ENERGETIC GND-BASED HARDENING IN SINGLE CRYSTALS

Swantje Bargmann
Institute of Mechanics, Dortmund University of Technology, Germany
Bob Svendsen
Material Mechanics, Juelich Aachen Research Alliance, RWTH Aachen University

ABSTRACT

In this work, a model for energetic hardening due to deformation incompatibility at large deformation is formulated in the context of continuum thermodynamics and extended crystal plasticity. In particular, this is carried out using a rate variational approach for the corresponding initial boundary value problem. This involves, in particular, the formulation of rate potentials whose form is determined in general by that of (i) the free energy density for energetic processes, (ii) the dissipation potential for kinetic processes, (iii) the boundary conditions, and (iv) the evolution relations for the internal variablelike quantities on which the free energy and dissipation potential depend. In the current context, these latter quantities include, for example, the inelastic local deformation and dislocation densities, in particular for geometrically necessary dislocations. The algorithmic formulation of the resulting model is carried out with the help of direct, and discrete variational, explicit time integration methods. To demonstrate that the model indeed predicts lengths-cale-dependent hardening behavior, simulation results are shown for the case of a 16-grain synthetic crystalline aggregate in two dimensions.

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