The continuum dislocation dynamics framework for mesoscale plasticity is intended to capture the dislocation density evolution and the deformation of crystals when subjected to mechanical loading. It does so by solving a set of transport equations for dislocations concurrently with crystal mechanics equations, with the latter being cast in the form of an eigenstrain problem. Incorporating dislocation reactions in the dislocation transport equations is essential for making such continuum dislocation dynamics predictive. A formulation is proposed to incorporate dislocation reactions in the transport equations of the vector density-based continuum dislocation dynamics. This formulation aims to rigorously enforce dislocation line continuity using the concept of virtual dislocations that close all dislocation loops involved in cross slip, annihilation, and glissile and sessile junction reactions. The addition of virtual dislocations enables us to accurately enforce the divergence free condition upon the numerical solution of the dislocation transport equations for all slip systems individually. A set of tests were performed to illustrate the accuracy of the formulation and the solution of the transport equations within the vector density-based continuum dislocation dynamics. Comparing the results from these tests with an earlier approach in which the divergence free constraint was enforced on the total dislocation density tensor or the sum of two densities when only cross slip is considered shows that the new approach yields highly accurate results. Bulk simulations were performed for a face centered cubic crystal based on the new formulation and the results were compared with discrete dislocation dynamics predictions of the same. The microstructural features obtained from continuum dislocation dynamics were also analyzed with reference to relevant experimental observations.

用于中尺度可塑性的连续位错动力学框架旨在捕获位错密度的演变以及在承受机械载荷时晶体的变形。它是通过与晶力学方程同时求解一组位错的输运方程来实现的，后者以特征应变问题的形式铸造。将位错反应纳入位错迁移方程中对于使此类连续体位错动力学具有预测性至关重要。提出了将位错反应纳入基于矢量密度的连续体位错动力学的输运方程中的公式。此公式旨在使用虚拟位错的概念严格执行位错线的连续性，该位错关闭了与交叉滑移，an灭，以及轻快和无蒂的连接反应。虚拟位错的添加使我们能够根据所有滑移系统的位错输运方程的数值解准确地实施无散度条件。进行了一组测试，以说明在基于矢量密度的连续位错动力学中，配制剂的准确性和运输方程的解。将这些测试的结果与一种较早的方法进行比较，在这种方法中，当仅考虑交叉滑移时，对总位错密度张量或两个密度的总和施加了无散度约束，这表明新方法可产生高度准确的结果。基于新配方对面心立方晶体进行了批量模拟，并将结果与​​该晶体的离散位错动力学预测进行了比较。从连续位错动力学获得的微观结构特征也参考相关的实验观察进行了分析。