Constitutive laws for continuum dislocation dynamics

在这个项目中，我们的目标是将位错-位错相互作用和位错反应的连续位错动力学（CDD）的本构方程。CDD的本构关系定义了平均位错速度对当前应力和位错状态的依赖性。本构建模应采用双重策略，结合自上而下的变分方法和基于离散位错数据的自下而上的方法。变分方法用于推导出弹性相互作用的表达式，其中捕获，例如，应变梯度效应。自下而上的方法的目标在经典的应变硬化，并使用离散位错模拟的位错反应和结形成的统计数据。此外，位错反应导致的位错增殖应纳入本构关系。推导出的位错通量方程应纳入有限元代码中，以便将预测与微观实验和离散位错模拟进行比较。

In this project we aim at incorporating dislocation--dislocation interactions and dislocation reactions in the constitutive equations for continuum dislocation dynamics (CDD). A constitutive law for CDD defines the dependence of the average dislocation velocity on the current stress and dislocation state. The constitutive modeling shall be achieved in a double strategy combining a top down variational approach and bottom up methods built on discrete dislocation data. The variational methods are used to derive expressions for elastic interactions which capture, for example, strain gradient effects. The bottom up approach targets at classical strain hardening and uses statistical data on dislocation reactions and junction formation from discrete dislocation simulations. Moreover, dislocation multiplication resulting from dislocation reactions shall be incorporated in the constitutive law. The derived dislocation flux equations shall be incorporated in a finite-element code in order to compare the predictions to micro-experiments and discrete dislocation simulations.