A mesoscale continuum approach of dislocation dynamics and the approximation by a Runge-Kutta discontinuous Galerkin method

We consider a mesoscale continuum model for the evolution of dislocation density in small-strain crystal plasticity. The model is based on the continuum dislocation dynamics theory and extended by a formulation for impenetrable grain boundaries. We introduce a fully coupled numerical method combinin...

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Bibliographic Details
Published in:International journal of plasticity 2019-09, Vol.120, p.248-261
Main Authors: Schulz, Katrin, Wagner, Lydia, Wieners, Christian
Format: Article
Language:English
Subjects:
A. dislocations
A. grain boundaries
Approximation
B. crystal plasticity
C. finite elements
Continuum modeling
Discontinuous galerkin method
Dislocation density
Elastoplasticity
Finite element method
Galerkin method
Grain boundaries
Mathematical analysis
Mathematical models
Numerical methods
Runge-Kutta method
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Summary:We consider a mesoscale continuum model for the evolution of dislocation density in small-strain crystal plasticity. The model is based on the continuum dislocation dynamics theory and extended by a formulation for impenetrable grain boundaries. We introduce a fully coupled numerical method combining a conforming finite element approximation of elasto-plasticity with an implicit Runge-Kutta discontinuous Galerkin discretization of the dislocation microstructure which allows for 3d computations including multiple slip systems and dislocation interaction. In addition, a numerical representation of grain boundaries impenetrable to dislocation flux is considered within this framework. The formulation is applied to a tricrystal focusing on the analysis of dislocation stress interaction between different grains. The results are compared to discrete dislocation dynamics data from the literature. •The presented model introduces a mesoscale continuum approach that accounts for the evolution of dislocation density in small-strain crystal plasticity.•The model incorporates a fully coupled numerical method combining a conforming finite element approximation of elasto-plasticity with an implicit Runge-Kutta discontinuous Galerkin discretization of the dislocation microstructure.•The formulation is complemented by a numerical representation of impenetrable grain boundaries.•It is shown, that the approach allows for a meaningful computation of 3d multi-slip systems and dislocation stress interaction inside as well as between different grains.•The results of a fcc tri-crystal with aligned grains under tensile loading show that the grain boundary as well as the characteristic dislocation pile-up behavior is well represented in the approach close to DDD data.
ISSN:0749-6419
1879-2154
DOI:10.1016/j.ijplas.2019.05.003