Efficient Numerical Solution Methods for Dislocation based Plasticity

我们将开发有效的近似和并行解决方案的单晶小应变弹塑性在3D中，其中塑性应变是由平均连续位错密度（CDD）的研究小组开发的系统。在每个滑移系内，CDD模型的龙格-库塔间断伽辽金方法将被实现，该方法描述了位错密度、GND密度矢量和曲率密度的演化。变形，取决于塑性剪切应变确定的Orowan的关系，然后近似与有限元。我们的目标是一个强大的和稳定的算法的耦合的整个系统，结合这两个模型，并允许大规模的模拟与全套slip system.The数值实施的CDD模型将基于数值方法开发的第一个资金期，其中hdCDD模型在扩展的配置空间被认为是;将比较完整模型和简化模型的结果，并对一个或两个活动滑移系的二维简化模型进行比较。位错速度的材料定律，不同滑移系之间位错密度的相互作用，并与研究小组的项目伙伴密切合作，推导出合适的位错边界条件，然后进行数值评估。

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.