Efficient Numerical Solution Methods for Dislocation based Plasticity

• Applicant: Professor Dr. Christian Wieners
• Subject Area: Mechanical Properties of Metallic Materials and their Microstructural Origins
• Term: from 2011 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 189971049

We will develop efficient approximations and parallel solution methods for single-crystal small strain elasto-plasticity in 3D, where the plastic strain is determined by the averaged continuum dislocation density (CDD) system developed in the research group. Within each slip system, a Runge-Kutta discontinuous Galerkin method for the CDD model will be realized, which describes the evolution of the dislocation density, the GND density vector, and the curvature density. The deformation, depending on the plastic shear strain determined by Orowan's relation, is then approximated with finite elements. We aim for a robust and stable algorithm for the coupling of the full system which combines the two models, and which allows for large-scale simulations with a full set of slip systems.The numerical implementation of the CDD model will be based on the numerical methods developed in the first funding period, where the hdCDD model in the extended configuration space is considered; the results of the full and the reduced models will be compared for a 2D reduction with one or two active slip systems.The material law for the dislocation velocity, the interaction of the dislocation densities between different slip systems, and appropriate boundary conditions for the dislocations will be derived then evaluated numerically in close cooperation with the project partners in the research group.

• DFG Programme: Research Units
• Subproject of: FOR 1650: Dislocation Based Plasticity