Abstract 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.

中文翻译：

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位错动力学的中尺度连续介质方法和 Runge-Kutta 不连续伽辽金方法的近似

摘要 我们考虑了小应变晶体塑性中位错密度演化的中尺度连续介质模型。该模型基于连续位错动力学理论，并通过不可穿透晶界的公式进行扩展。我们引入了一种完全耦合的数值方法，该方法将弹塑性的一致有限元近似与位错微结构的隐式 Runge-Kutta 不连续伽辽金离散相结合，允许进行 3d 计算，包括多个滑移系统和位错相互作用。此外，在该框架内考虑了位错通量无法穿透的晶界的数值表示。该公式应用于三晶，重点分析不同晶粒之间的位错应力相互作用。